I've found an issue that seems to be present across multiple titles i've tried so far.
On macOS, launch a game without a game center
Open the GameCenter Access Point overlay (or wait for an auto sign in prompt)
Choose "Sign in with another account"
Enter a valid AppleID email address
Enter an incorrect password so the login fails
The GC prompt then locks up, the password field can't be edited and the pop-up cannot be closed. Pressing cmd+Q does not close the application
This occurs on multiple systems running macOS 12.3 but not on a system with macOS 11.3
Anyone else experienced this and found a workaround, or is the Gamecenter login just broken?