google_sign_in_android has a bunch of Dart logic to work around the fact that the updated sign-in SDK on Android didn't have the same ID token that all the other SDKs have. However, based on flutter/packages#11694 it appears that v 1.6 of the SDK added the field we wanted.

We need to validate that it is indeed the same ID that we are manually extracting, and if so, remove all that Dart code in favor of using the now-SDK-provided ID.

(Triaging to team-android in case I don't end up doing it, but assigning to myself since I'm very familiar with this code, and would be happy to simplify it.)