How to unlink game from Game Center

I’m trying to delete an old Simcity build it game that was saved to the Game Center so I can link my newer game. All of the information on this forum suggests I should be able to go to settings > iCloud > manage data > [app name, click to delete], but when I go to manage data, none of my games are listed, even the ones linked to Game Center. This is extremely frustrating, and I do not want to be forced to either go back and regain my new progress on a save game from 2015 (it is currently December 2021, old game), and if I create a new Game Center account, I will have to restart all of my other games. I just want to be able to see simcity in the game center widget with the rest of my games for easy access. How to unlink Game Center to link the new game?