Same issue here, tried on Monterey and Big Sur with Xcode Version 13.1 (13A1030d)

Looks like it works again without any changes done on my side.

Xcode 13.4.1 is not working even from terminal: it says: The application cannot be opened for an unexpected reason, error=Error Domain=NSOSStatusErrorDomain Code=-10664 "kLSIncompatibleApplicationVersionErr: The app is incompatible with the current OS" UserInfo={_LSLine=3945, _LSFunction=_LSOpenStuffCallLocal}