I’m also experiencing the same issue with Game Center not recognising the app and unable to authenticate local player or load leaderboards.
Have set up the app in Xcode and Apple Connect exactly as Apple recommend.
I submitted a Technical Support Incident (TSI) via the developer website. They only responded a week later to tell me to submit a bug report via the Feedback Assistant.
That was over two weeks ago and I’ve heard nothing.
I’ve even downloaded the sample project from the following Apple video, but it still doesn’t work.
https://developer.apple.com/videos/play/wwdc2021/10067/
It’s really very frustrating to say the least!!