When you get some time, could you try rebooting, starting the itch app, and trying to log in again?
I’ve gotten some more confirmations that the update did indeed fix that particular problem (the “x509” message), so I’m more and more surprised it’s not fixed for you.
A last minute theory could be that even though the files were deleted on disk, the older version was still running, and the installer “brought it to front” instead of starting a fresh copy of the app. (*nix systems like macOS don’t have problems with executable files being removed while they’re running, unlike on Windows)