Good Day Gabriele06,
My name is Carlo, I am also using Windows 11 pc and community member like you. Let us work together to sort this out.
Here's the steps you can try.
-Click start, type Powershell and run it as administrator
-Copy and paste each of the commands below and hit Enter
get-appxpackage Microsoft.GamingServices | remove-AppxPackage –allusers
start ms-windows-store://pdp/?productid=9MWPM2CQNLHN
That will open the Gaming Services page in MS Store when you press Enter.
Then click Get to reinstall Game Services.
You should see a progress bar that will be the Windows Store re-registering itself with Windows 10.
Restart once done and check.
Have a wonderful day ahead and stay safe.
Sincerely,
Carlo T.