Unable to remove Game Center internet accounts

I've noticed that I have 2 internet accounts for Game Center. One is for iCloud, the other for an old and cancelled btinternet account. I cannot remove them in System Preferences by selecting and pressing the '-' option and they are unresponsive and do not mirror any simple changes I make to Game Center on my iOS devices e.g. changing my User Name. This means that I am not able to use Game Center on the MacBook.

Game Center appears to function normally on my iOS devices. I have tried removing the accounts from the MacBook in Safe Mode but there's no difference to trying in normal mode - nothing happens. I also tried a re-installation of Big Sur but that had no effect.

I've researched the problem online and the only potential solution I can see is to manually delete files in the MailData folder and Accounts.plist. I am not confident enough in my own abilities to carry this out without making a muddle of things.

I'm using a MacBook Air M1 running Big Sur, and this was set up using a Time Machine backup of a previous MacBook Air (early 2014) that I sold when I obtained this machine.