I was in-game just fine ten minutes ago. I restarted my console and was about to get back in-game with a friend and we both are getting the same errors - first is from ESO itself in the sidebar where characters normally would be listed:

LOADING PROFILE FAILED
You do not currently have network connectivity. This title requires a Sony Entertainment Network Account and a network connection.


And then the PS4 gives this error over top:

Cannot connect to server so network features for this application unavailable.


Both of us have active and working connections (we've tested them, power-cycled modems etc) and both have active PS+ accounts. It's not our ISP, we've looked into that. I searched for this same error and saw it was a problem back in June, so I'm guessing it's on ESO's end? I can't find anything posted about it [today] on any of the places I'd look normally: Reddit, Twitter, this forum or any server status issues.