Saved credentials are out of date. Please re-enter your password.

I see that every time I try to log in, even though it shows [Saved Login Details] in the password box and I have Remember Me checked.

I have same problem (standalone client - no Steam/Epic)

I've found solution.
If you have linked sub-accounts (for example Normal account + Steam account) then you need to log in on both accounts:

1. Enter your password and log in;
2. Switch to your second sub-account (it is drop-down list in upper right corner on character selection screen), you will probably get kicked back to login screen and get same message about out of date credentials;
3. Enter your password again (Have checked "Remember me" ON) and log in;
4. Now you can switch back to your first sub-account.

Oh that's really cool. It's a workaround to something that still needs fixing, but that would explain why the issue suddenly went away when I made a character on the other sub account.