LoginWithGoogleAccount is obsolete. The official Google Play Games Services plugin (
https://github.com/playgameservices/play-games-plugin-for-unity) wants you using
PlayGamesPlatform.Instance.GetServerAuthCode to get an auth code that can be exchanged for an access token on the server.
Trying to call the obsolete GetAccessToken brings up an additional popup in the app asking which account to use, even though you are already signed in to Google Play Games. It makes it very confusing for the user and will increase drop off rates.
I don't understand why you have not updated your API. You should not be months behind Google and Apple on their APIs, it makes you look bad. As of right now I have no cloud functions on the Android version of my game and won't until this is updated to use the new approach.
Thanks.