Play game auth not merge account with google signin and doesn't get PhotoUrl

I have firebase init user with google play game server auth code successfully. However even there was the same user with google account and I have set preventing authenticate multiple account with the same email, it still result in separate ID and doesn't merge with existing user

And PhotoUrl is `null` when authenticate with play game service. It should return at least the `PlayGamesPlatform.Instance.GetUserImageUrl()`

Are these the expected behaviour of play game auth?

Reproduce Firebase initialization with a Google Play Games server auth code and an existing Google account using the same email. Inspect the resulting user IDs and PhotoUrl, then compare PhotoUrl with PlayGamesPlatform.Instance.GetUserImageUrl(). Done means the expected account-linking and photo behavior is documented or the discrepancy is isolated.

Written by the indexing model from the issue text.