Game won't connect to Game Center

I play a game on my iPad Pro (Theme Park Tycoon by Codi Games). They have an option for connecting to Game Center in the game. It shows in the app that it's connected, but when I sign out of Game Center and sign back in through the app, it says that the app is not supported by Game Center. All of their other games work for me when syncing to Game Center so I can also play it on my iPhone 12 mini on the go, but not this one. I have contacted the developer to see if this is an issue on their end, but they could not find any issues on their end. Now I am wondering how I can get Game Center to recognize my game so I can switch between devices without having to start over on the second device.