I've just been playing on PC EU (direct through ZOS) with no issues, including zoning between wayshrines a few times. Plenty of other players logged in. I'm using the original launcher, not the new beta one.
Maybe you need to repair your launcher files and try again. I assume there's a Steam discussion forum where you could also check if anyone else has the problem, if it is persisting (it may just be a one-off).
Also on PC EU playing through Steam and since the update last week have been constantly kicked from the game (losing several EA runs) and getting the unexpected internal server error repeatedly when trying to get back in.