On the official documentation of Firebase Authentication, the guide is only available on how you can get the googleAccessToken on native Android & iOS. No solution is available for Unity on their official guide.

The closest solution I have found is to use the Google Play Services plugin for Unity to get the access token, which is not a good solution for the cross-platform as the following plugin is deprecated on the iOS platform. So yah, your code will not work on iOS.
Also, I believe it's an expensive solution to add a plugin for a "googleIdToken".