I'm locking this chat now as a lot of discussion has gone on, and there are many work arounds to this, but none of which are entirely fixing the issue at heart. I think even without the nightly image this method should work with the stable release. Login back using the v1.13 stable release.

From there the login was successful once approved the access. Clicked the Try again button a bunch of times until I got the enter password page, it then took me the approve app access via the 2FA auth section.Download the latest v1.14 nightly (appimage) and open the app.This method appears to somewhat work with the v1.13.0 stable release too, on my linuxmint 20.2 system. I'm pentester and sometimes I just keep clicking next a bunch of times to see what happens.

TL DR - just keep clicking 'Try Again' on the google login prompt until it works. My theory: There's probably some kind of fail open trigger that temp disables the 'out of date browser control' on the account level if you trigger it too many times. It's (likely) the Google login page failing open vs closed (my theory anyways). Just kept clicking 'Try Again' in the on the google login prompt, 6-7 times after it logged me in. Fresh install of 1.14.1 nightly on Windows 11 21H2/22000.348 (verified the appdata roaming folder was removed)

Least insecure browser