Square-Enix.com. I created the account already for Tomb Raider, never played FFIV. On the website there's an option to link your PSN account, which I had already done.
When I try to login via the game I get "User ID and password do not match."
Ugh.
I actually had to create a new account, and I already had one from FFXIV 1.0 (complete with authenticator). I could log into the website just fine, but the same credentials wouldn't work in the PS4 client, even after removing the authenticator.