I have an Xcode project under git version control (github). I recently had changed the github user name. Xcode detects the name change and shows it correctly under Settings/accounts. Push and pull still work as expected.
When I tried to configure Xcode Cloud I got an error message similar to '...Xcode Cloud could not connect with your source control provider...' during initial setup procedure. [1]
The solution for me has been to edit the git config file, updating the URL for [remote "origin"] to the new path reflecting the new git user name.
I would have expected that Xcode would have updated this config file when recognising the github user name change.
[1] A exact German language error has been:
"Die Verbindung von Xcode Cloud mit Ihrem Quellcodeverwaltungsanbieter konnte nicht erstellt werden. Versuchen Sie den Einrichtungsablauf erneut, um Xcode Cloud Zugriff auf Ihren Quellcode zu gewähren. Weiter in Xcode"