If you want to DPS too then Altmer, if you want to pure heal to the best of your ability then Argonian.

Argonians: 9% max health which translates to 1-1.3k health depending on your build. With witch mothers brew and 1 health glyph on an infused piece (large) you sit at 17.1k health which is fine for most current endgame pve content. Very small 5% healing bonus translating to almost nothing on heals ranging in 2-3k range. (Healing springs, quick siphon crits,). Breath of life gets its job done with or without a 5% increase as a life saving heal no longer spammable post morrowind.

High elf: 10% max magicka, 10% recovery, no max health. You will be at 16k ish without the 9% health, meaning you have to replace a large magicka glyph with a health glyph. Goodbye 10% magicka because you can't feasibly run content with 16k health (HM trials) unless you're on a good performing PC with addons.

The point is there used to be a major difference pre morrowind and high elf outperformed argonians by a lot, but now every race sucks and it doesn't matter which one you pick

Even over the course of the longest boss fights and hardest fights in the game your decision making and how you
Manage your own resources and select when to do what matters WAY more than any racial passives. Good people can make bad races perform well and Vica versa.

Breton is in my opinion the best choice for healer. 3% cost reduction is huge with the spell costs a healer has and the increased spell resistance is very useful since you want to be a vampire and it counters the weakness to fire.

Highelf is second place in my opinion. Since another 10% regen stacks very well on a healer, but the rest of it's passives isn't too great.

Argonian is very strong on paper but I wouldn't recommend it. Healing done is okayish in PvP, but useless in PvE since your heals are already so strong from your base stats that you overheal. The potion thing is very strong, but in my opinion it requires you to take potions on cooldown or when you run dry, which you don't want to do in my opinion. I use potions in situations where I need a certain buff like immovable. A potion based sustain is also bad if you want to do easier contend in my opinion since you waste potions in situations where you wouldn't even need one with another race. You also have no use for the HP and pretty much none for the stamina in a lot of situations.

Okay, I've gone for Altmer for my healer. Sorry for the late reply and thanks for the input, guys.

I'm curious, though - I'm gonna remake my tank that I started the game with but I hear good things about Argonians... is it worth going with an Argonian DK or going with an Imperial?