Recovering very old GameCenter not linked with email

I used to use a GameCenter account that only had a username. This was back when GameCenter was a separate app not just linked to the Apple ID or an email. As a result, when I encountered an issue signing in one time, it wouldn't allow me recover account.

I could not recover my game stats since I was unable to open the game. The game developers had stopped supporting older devices like my iPad mini 1 and iPhone 5s. It's been years since I actively tried to recover it since I have not had helpful responses in the past. Has anyone had any luck recovering these super old GameCenters?

I just want to recover the data before my ancient devices stop working permanently.