Upgrade Firebase Google sign-in to Credential Manager SDK (current method deprecated)

[DiplomaticRobot]

Migrate Google sign-in integration to the new Credential Manager SDK as the current method is deprecated. Update Firebase Auth dependencies and authentication flow to use the officially supported approach.

References:

• https://firebase.google.com/docs/auth/android/google-signin
• https://developer.android.com/identity/sign-in/legacy-gsi-migration