How do I know my Game Center email and password?

Hi, I have a problem with my Game Center account: both the email and password of a game account I access via Game Center are different from my apple ID and apple ID password, the problem is that I don't know either of them as they were randomly generated and are not saved anywhere.

This problem results in me not being able to access my game account (in this case my Genshin Impact account) from another apple device other than my iPad because I do not know either the password or the email. Is there any way to trace back both, or is it possible to change the email associated with my account without first logging into my current email (the one that I don't know) and without losing all my game progress?

thank you in case of reply