I read much about the dreaded cuts to the healer role in the classes in several threads and decided to check some things for myself.
Well, there are some common things all healers have as I noticed playing all classes as healers in ESO. These I checked first.
I checked 2 classes -Templar and Dragonknight- throughroughly and the rest in gear checks, theory and calculations so far on the PTS and I want to give my 2 cent about it to you all and the devs.:
I have to verify the rest of the classes as well with the general findings I got on the first 2 classes and the meta there, but it looks promising.

First of all, many wrote they would have to use braindead Rotations as DDs do:
Well, yes and no.

If you really used all your means as a healer, you already had rotation parts you could use for higher heal output, but you could very well do without them using some tweaks or easier ways like spamming of energy orbs and stacking of Grand Healing and its morphs, but the Heal was adjusted and Skills were changed to make this up. But you have to decide if you want to heal or do good damage.
As an example for this I used as a templar the following rough queue in the old patch (annotations for the new rotation and maths about it are added in brackets):
Pre-Hotting with Rapid Regeneration and initial Minor Berserk Buffing with Combat Prayer on the way to the next ob group or boss. Using a sunfire morph for minor sorcery (buffing the group) and myself with Major Prophecy and generating ultimate, if I was the only templar in the trial I would use Power of the Light instead for Minor Breach and Minor Fracture. Then I'd use either a potion for Major Sorcery or the mages Guild skill structured Entropy to do the same.
This results alone in a net bonus of Minor Berserk (+8% Damage -don't let the name fool you, weapon/spell damage is also healing and it is confirmed to add to the healing of the used resource pool for HoTs and Direct Heals.) plus Minor Sorcery (+10% Spell Damage - also plus Heal ) plus Major Sorcery (+20% Spell Damage).
This will push the following Cleansing Ritual Morph Healing by 38% -this is all additive atm, but it will be multiplicative, which will be a bit higher-, which adds plus 8% Healing due to Minor Mending (Sacred Ground Passive) and of course the +0 to +12% of the passive (Mending) for missing Health on Players.
After this, a full heavy attack with your healing staff pushes it further by Major Mending (+25% Heal) for 3 Seconds.
You want to lay your biggest aoe-hot-heals first in this condition, which means you may have to recast Combat Prayer by now, if not, just use your Cleansing Ritual Morph and revel in the numbers, while using one of the following as you need it: Grand Healing Morph / Panacea Morph / Rite of Passage Morph / Regeneration Morph or Energy Orb (both today preferably spammed to get as many with the highest bonus as it will mostly retain its bonus it had on cast time in future the Orb would be one of the first ones used after the Ritual).
If you need it, you can use this as a starting point for single heals and regeneration by heavy attacks (remember the +25% Heal for 3 Seconds if something has to be renewed) or even damage with Puncturing Strikes Morph or Support with Luminous Shards.
If there is not the time for the whole rotation, I'd start with Combat Prayer, Cleansing Ritual Morph(if needed) or another big heal and when the situation is more stable to return to the normal rotation.
Things like Major/Minor Sorcery and Minor Mending have a long uptime, so these are the ones to keep up, the other ones are weaved into it.

Grand Healing was very versatile for healing people outside of the major healing zones, as was the Energy Orb and the long running Regeneration Morphs.
The Devs took that versatility away to force DD Classes to take a self heal into their bar, as some did not have that for damage rotation.
Since Vigor was balanced for those versatile heals from Healers, it is now buffed, which makes Stamina Healers more viable than ever.
Every Class seems to have an aoe heal of at least 5 m reach (DK Cinder Storm, NC Life amid Death, WD Life Bloom, SC Power Surge 2.6k on crit ~ should be out in the same ball park, but I'd have to check high rotation times), that is on par with the raw healing of the Circle of protection (5m reach, but 0.5 second steps) as well as with the healing of the illustrious healing with 8 m reach ~1.6k per second. The energy orb is movable with about 2/3 of the hot of the other aoe circles, but it can be synergized more than once and heals roughly 7.5k without any modifying buffs.
As a side notice, the rushed ceremony morphs of the templar, which were the bread and butter spam to reach someone in need are pretty useless as of now, as you can only reach someone who is in sight. So for the biggest healing aoe hot circle they lost the undirected rescue heal.

As a Healer I'd want those 2 Heals (Vigor and Ring of Preservation) badly, as they are good, but they do not scale well with magicka, even with the Set Pelinal (Spell Damage and Weapon Damage are set to the highest of both values) for Templar and Dragon Knight, they remain at the bottom end and are 1/2 to 1/3 of the Healing of a Stamina DD, though they are slightly better then without Pelinal. They are tools to work with, but with the danger of loosing survivability, so you'd have to use each only once in a rotation to give the stamina Pool time to regenerate or you have other means to regen Stamina.

Well, I could use my Rotation Fragments well for the group healing, but it takes a lot of foresight and battle awareness to pull this off and your versatility to keep people alive outside of your main heal zone is limited. The actual heal with the usage of the bonuses is pretty much the same, if not higher, but it takes more effort. 4 times stacking Grand Healing in old times meant solid 4.8 k heal, now you have to use about 3-4 skills with 1.6 k heal and scale them up with those buffs which will be at ~50% realistically if things get hectic in a fight. But that means, 2 skills would suffice to reach the same heal output. You can stack them higher or you could still use one of your circles to help out someone outside and in spike you can get much higher with your heal.


For the other Healer option I hinted at: I noticed that if you use the Pelinal Set with Stamina as your Main Pool (for Templars and Dragon Knights), Magicka Healing Skills scale better with this Set than the other way around in the newest patch. (Weirdly enough, this is not the case with Wardens, they work with either Pool just fine as main Pool. Have to test it for Necros, Sorcs and Nightblades again) It is slightly lower in Magicka Heal than a pure Magicka Healer, but you gain the full force of the Stamina Heals and you use both pools, meaning one is regenerating when you use the other and you can always regenerate resources actively.
If you want to use such a hybrid build as a new Stamina Healer you need to change from light Armor to Medium Armor pushing your Weapon Damage (and heal) by 15%, but loosing 20-28% Magicka Regen and 10-14% Magicka Cost and Spell Crit and Penetration are down.
Also you need a means to regenerate stamina actively and push that weapon damage and Healing further up. So Dual Wield Swords are not too bad for this and on your second utility bar you need your Restoration Staff (Asylum Sanctorium is best in slot for obvious reasons [-30% cost for 3 sec], but not necessary).
Since the formula for all skills looks a lot like this x(Main Resource or Fixed Resource) + y(Spell or Weapon Damage) + z(Constant Value for Skill or Type of Skill) we want to have Stamina as Main Resource, but enough Magicka to actually do something with it and the regen to go with it.
So we take Stamina as Main Stat in Attributes and use Tristat Runes on all the Armor Parts we have and end up with 21k Mag, 20k Health and 31k Stam.
The Pelinal Set itself would be done with invigorating trait to replace the lost regeneration and the Monster Set could be free or also with it. Feel free to do as you like, Argonians could easily take other traits for instance, as I will mention below.
Sets with 6% cost reduction for all are pretty good with this build, but Champion of the Hist is also a thing to think about, as you could fill up your ult faster and use it to heal/buff(e.g. with Life Giver Morph) and even lose the Combat Prayer from the Skill bar as it is included in Life Giver.
Even Heem-Jas' Retribution could work well in some trials with constant trash in fights, as Major Berserk also pushes the heal.

This Set uses those Race Bonuses best:
Dark Elves (Mag and Stam Pool + Weapon/Spell Damage +++
Redguard (Stam Pool and Stam Cost Reduction) ++
Khajit (Regen, All Pools and Crit Heal) +++
Nord(Stam Pool and Ult Regen) +
Breton (Mag Pool, Mag Recovery, Mag Cost) ++
Argonian(Tristat Potion for free, Mag Pool, +6 % Heal) +++
Bosmer(Stam Pool and Recovery) +
Altmer(Recharge works both ways, Mag Pool, Spell Damage is lost due to Pelinal Mechanic afaik or you'd have to base its Pool on Magicka) ++
Orismer(Stam Pool, Weapon Damage) +++

Monster Sets could be Balorgh or Molag Kena (or the Combination of both) or any other suitable weapon/spell damage or Heal Set.
The result is a set, that gets you with damage plus race passives, damage enchantments and damage buffs a really good 5 tier damage/healing bonus, while using both Pools with good regeneration.
Not enough to switch all healers to Stamina Heal or even the set though, but it works well and has a large healing output.


Now for the Rotation Fragments of the other classes that should work:
Dragon Knight
Ignaeous Weapon (Major Sorcery and/or Brutality +20%) holds 42 seconds as a starter, Cauterize (Major Prophecy for crit heals and Heal or Savagery with the other Morph as Stam Healer), Fragmented Shield ( Major Mending +25% Healing, +Minor Brutaliy +10% Weapon Damage for Group with Passive,+ ult generation) could be swapped with Heavy Resto Staff Attack if needed for Major Mending for 3 Seconds, Combat Prayer/Life Giver(Minor Berserk +8% Damage), Illustrious Healing, Cinder Storm, Echoing Vigor, Ring of Preservation, Energy Orb (most likely 2 of those mentioned after Combat Prayer are missing out for other skills, but they are pretty exchangable, not the Orb for trial regen though!). Rescue Options would be Obsidian Shard as a directed heal to help out, Magma Shield or Life Giver ult, or the fragmented Shield again with Heavy Resto Attack (it also heals, remember this)
This is straightforward and pretty easy to play, but the diected heal via damage on an enemy is a pain in the ass. I'd just swap it for Healing Ward, just to loose the bother there.

Nightblade
This is an odd one, but funny as hell.
Drink Weapon Damage Potion for initial Buff of Major Brutality, set Reapers Mark on a mob most likely to die fast for Major Berserk(+25% Damage -and heal, just as a reminder for jumping readers) and for Minor Savagery for the group, when you deal critical damage with the skill in bar, Heavy Resto Staff Attack for heal and Major Mending (+25% Healing done) for 3 seconds (can be switched with Healthy Offering and vice versa, if a fast big heal is needed), Healthy Offering for direct heal and Minor Mending (+8% Healing)+ ult regen + 3% Heal +8% Max Magicka for skill in slot, Sap Essence for aoe damage and Heal and Major Sorcery (+20% Spell Damage), Refreshing Path for a large healing area half of hps of what similar aoe hot circles would do -but with the boon of Major Ward and Resolve + 3% Health for you and Major Expedition of your Group Members, Combat Prayer for Heal and Minor Berserk(+8% Damage), Grand Healing Morph, Ring of Preservation, Echoing Vigor, Energy Orb. Spammables would be Funnel Health (good to trigger the minor Savagery for the Group as mentioned before) or Regeneration Morph here as a big direct heal is missing here. Rescue Options are Bolstering Darkness for a large synergy heal + Major Protection (+30% Damge Reduction), Soul Siphon for plain heal/hot and synergy damage/hot and Major Vitality (+30% Healing received), Healing Ward, Life Giver.
This is one of the harder Rotations as you have not much time to bring out your best healing circles and the reapers mark buff can be pretty rng. But it is a nice utility buff for the group and welcome extra damage and heal. But instead you have the best Healing and Damage Reduction Buffs in the game at your disposal with a really high ultimate regeneration to begin with. Spam with them, you have it. After using them is a perfect time to refresh refreshing path, you can go higher than 100% bonus with your buffs, making it one of the largest healing zone skills with around 1.6k hps buffed. All spells after it just go higher in their zones as well, ring of preservation would top of at 3.2k hps and Vigor reaches even higher.

Sorcerer
Well, Sorc Healers are really a strange thing, and it is best to see their class heal abilities as supporting abilities (they are strong as hell though). Mainly it is Power Surge as a Buff of Major Brutality and Sorcery for yourself, which lets you heal around 3k hps if you crit every second.
I still have to measure its reach, but it seems farther than the usual 5 m here. The Absorption Field Ult heals with ~2.4k hps in 8 m radius. Twilight Matriarch will heal 2 for ~6k , but it has to be summoned and is not viable in some fights.
Bound Aegis is a self shield and max Magicka Buff (+8%) and gives by passive +8% Health + 20% Health and Stamina Regen. Empowered Ward is just a group Buff for 10 Seconds for Minor Intellect (+10% Magicka regen) .
Each class ability slotted pushes Weapon and Spell Damage by +2% up to 12 %.
Makes a fickle design point there for a rotation and bar design. Any dark magic skill buffs the group with minor Prophecy (+spell crit).
This Class has the least native Bonuses for healing buffs, but the best survivability, if those skills are in the bar.

You might start with Power Surge and Lightning Flood there to get basic healing out.
NOTE: Combat Prayer with Minor Berserk, Major Berserk, the Nirnhoned Weapon Trait or magicka/stamina above the attribute pool do not affect this Skills Heal at all, but the Powered Weapon Trait affects it, making this officially a weird skill to have. A heavy resto staff attack (Major Mending 3 sec) just works for the 3 Seconds, making this basically worthless for Power Surge, but you could push the Heal with the Healer set of the Dragonstar Arena for Minor Mendings 8% (more Magicka is better though due to the Support Nature of the Build).

With this in place you could just go happliy about doing damage to deal crits and using Twilight Matriach Heals in little groups for rescue option or use single instances of Energy orb, Echoing Vigor, Grand Healing Morphs, Ring of Preservation, Healing Ward or Regeneration Morphs to heighten your ground Heal.

Any of these options may suffice and this class is the one of the best magicka support roles/DD in one person in my opinion. As you could easily pump out 3-4k hps to 7k hps (crit heals are possible!) while doing damage with just your power surge and your Absorption Field as support. The only thing that really sucks is that only powered would up Power Surge, but hey, due to the mechanism I'd take Precise and high CPs Points for Crit Heal instead.

In combination with Minor/Major Vitality of other classes you could push Power Surge above 4k per second for the runtime of it. Strange is this behaviour as many hots and Zones still retain their bonus got at cast time. This seems to rely on the buff nature of the heal, which is basically a reaction to the crit of your damage skill.
All plain Healing Bonuses change its heal, making the Naga Shaman and Hollowfang Thirst Sets really good sets for main healing Sorcs as they can push the heal up to 7k crits and 4k normal ticks. A combination of two Monster Sets for +8 % Healing done is also viable, but the damage goes down then and the heal upwards. Have to test it further.

The Twilight Matriarch still profits from the Berserk Buffs, but it is not shown in the skill description. When you cast under their influence, the heal is proportionally higher. This counts for the Absorption Field as well. It profits from Berserk and Major Mending for its whole runtime, so buff stacking is wise there.

This makes the Sorc one of the easiest and one of the hardest healers at the same time. Base design is support heal by crit dps and you heal people near yourself regardless of were your crit happens (lightning flood!!). Which is missing if you stack resto staff abilities to use them over damage skills. You might profit from other main healers Buffs, but you would have to have alerts for their usage on to bring out your hots/circles reactively as you do not have much to buff for yourself.
In sync played with a templar or nightblade healer for their buffs this could be very sweet, as it is high dps and good base heal for just 2 Slots "lost" for healing abilities.

Warden
The Warden has more native options in healing and buffing that are situative, but this makes it a strong heal stacking class as well. And it seems to never run out of resources if the netch is used well. And he has a great Ultimate Regeneration, which makes the Ult a viable Heal Rotation option.
Major Prophecy/Savagery from the Netch, automatic Major Mending from Heals under 40% Life of someone with Green Balance Skill Tree, Minor Berserk and Major Expedition from Bird of Prey, Major Mending from Resto Staff Heavy Attack, Minor Toughness and 250 Resource for the lowest Pool (every second) on all Green Balance Heals and Minor Intellect and Endurance on Enchanted Growth are the class/weapon options.
Prefight starting with Ice Fortress (Major Resolve/Ward for Group (8m), Minor Protection), Bull Netch(Major Sorcery/Brutality), Shimmering Shield(Major Heroism and Shield), Enchanted Growth(Minor Toughness), any Lotus Morph(+Heal on Attack for Group Heal), Combat Prayer/Life Giver (Minor Berserk), Healing Seed Morph. In fight Resto Heavy Attack (Major Mending), Combat Prayer/Life Giver(Minor Berserk, could be left out if Bird of Prey is on Bar), Healing Seed Morph/Ring of Preservation/Energy Orb/Echoing Vigor. Maybe Leeching Vines (Life Steal), Bursting Vines (Ult Regen) or even Combat Prayer/Life Giver again to keep Minor Berserk up (one of the options will likely be dropped from the bar, my money is on the Vines Skills in favor of RoP and Energy Orb). Then start over with Heavy Resto Attack. After 2-3 Rounds, recast Ice Fortress, Bull Netch, Shimmering Shield, Enchanted Growth, any Lotus Morph. Check your Buff Bar Addon for this.
Rescue Options are Healing Thicket, Northern Storm, Polar Wind, Enchanted Growth or Leeching Vines.
This is a straightforward Rotation. Anything in your sight lives, the rest dies to say it bluntly. Ok, some Heals can be placed, but it is harder to get rescue Heals to the victim of a pummeling. The Twilight Set from Maw of Lorkhaj might help as the Warden has many Synergy Skills, which can be used, if they are used and it provides minor force to the synergy healed.


For Necromancers I have to follow up later, but the basic principles should be the same for them as stated above.
Generally spoken, the Necro Corpse Mechanic can make it very strong in ultimate regen or HoT circles. The healing spirit needs debugging as it seems, as it has odd healing behaviour sometimes.(There are other threads which mention this, so I'll spare you the details.)

In Conclusion (tl;dr):
Not all is lost, Magicka Heal is still viable with basic Rotation Fragment Rules. Stamina/Magicka Hybrid Healing with Stamina as main pool with Pelinal Set is quite the easy mode for Templars or Dragon Knights. Wardens could use either Magicka or Stamina as Main Pool. Nightblades, Necroes and Sorcerers have to be checked up for this again. Some class heals are strengthened and normalized with aoe hot circles/zones to make them interchangeable with each other for switching the side effects of the heals. With Rotation you just need to stack 2-3 to reach the old hps, the rest is bonus as long as you are not a sorc. Sorcs are the best DD/Support Healers atm with Power Surge as long as they can do damage and crit. Nightblades are the hardest to play, but with the best buffs to the general healing. Templars have a nice circle heal, but lost their good recue heal. Dragon Knights have Shields, a 5m native hot circle, but a terrible rescue heal.

I hope this helps and gives a bit of food for thought to test other ideas and builds.