Very typical issues with those Apple framework & APIs, had problems for years and no one ever wanted to fix it.... Same here for me, I am guessing most likely not many people are using their GameCenter APIs (except for leaderboard & achievement). All serious developers or companies might already developer their own servers to avoid as much as possible their framework....

Really frustrating to deal with those kind of bugs. It's been there for years from the internet search, and yet it's still there! I feel like I paid the membership fee for nothing because my game would be multiplayer game. I have the exact same situation as @pjb1000 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.  Which I don't think they will look at it.... Very disappointed.