It depends on the addon. A lot of addons will be entirely unaffected because they don't relate to anything which is being changed by the update. For the ones that are affected some authors will be able to update their addons based on the PTS, some might not have enough time until after the update goes live, some might try to update it and then bugs are discovered on live which weren't present on PTS and those have to be fixed before it works and some might have left the game and will never update it.

The only way to find out in advance what's likely to happen with a specific addon is to ask the author, or see if they've already said something about it online somewhere.

But for what it's worth my approach is always to check for updates via Minion while I'm updating the game itself, start playing with out of date addons enabled and see what happens. If I get any problems I disable the offending addon (or all of them and then re-enable one at a time to find out which is the problem if it's not obvious) and keep it off until it's fixed. I make sure to check at least once a day for updates to addons and if not being able to use a specific addon gets to be a problem I'll go looking for an alternative but it's pretty rare that happens.

(I'm using a few which have been out of date for years now, but they still work. Binder is probably my personal record holder - it hasn't been updated since 2014, except for re-uploads with new version numbers. But it works and doesn't appear to cause any problems so I keep using it.)

You shouldn't use any addon that deals with Champion Points (like Champion Points Slot or Superstar) until they're updated for the new CP 2.0.

Also addons that automatically put Rapid Maneuvers to your bar when mounting up (like Fast Ride or Assist Rapid Riding) aren't needed anymore because Major Gallop is now worked into the first passive of the Assault skill line.

Also, Combat Cloud gave me permanent UI errors when fighting npcs at a ressource in Cyrodiil after patch.

I've been pleasantly surprised at the lack of breakage with this update. It's a nice change of pace.