Same issue with Ventura 13.2.1, Xbox Elite Controller perfectly well recognised by Bluetooth but games I tested such as Cat Quest II detects the GamePad but I cannot do anything... Only way is to quit the game and turn off Bluetooth then I can play with Keyboard (annoying as hell). This issue has been ongoing for more than a year......... I thought Apple was doing efforts to bring games to macOS since you can use softwares from iOS... M1 computers are great but seems abandoned for support on that side. Apple please..........

Had a similar issue. 2-3 USB devices working properly on any computer stopped working on a student computer. Struggled with searches then in Security I saw the student had the Firewall on...... Tried to turn off and apparently she made a setup to block USB connections !!!!! Since then I've been able to connect USB devices again. Took me an hour to figure this out....... And student next to me staring at her computer all the time.