Change Firebase project for produtive app with Google Authentication?

I need to change Firebase Project of productive app with google authentication.

My app is working with a firebase project and a backend server from which I can force users to update my app to the latest version after login with version the user has. Because of that, I hope I can change the Firebase project where I do the authentication with Google.

I can't use old pair Package Name / SHA-1 in new Firebase project, but I can use old package name with NEW SHA-1, right?

So, users with old versions will login with old firebase project and after upgrade my app they will login with with new firebase project, right?

If so, users won't need to uninstall my app, right?

Now, how can I change the SHA-1 in Android Studio?

from Change Firebase project for produtive app with Google Authentication?