Repository: flutter
Issue: [google_sign_in] iOS user get stuck on plugin auth screen if OAuth user type is internal
Labels: platform-ios,p: google_sign_in,package,P2,team-ios,triaged-ios

We have inner application and OAuth user type mode set to [internal](https://support.google.com/cloud/answer/10311615#user-type&zippy=%2Cinternal) on Google Cloud Platform. It means that account that does't belong to organization workspace can't sing in. But there is a problem if an iOS user singed in with such account and it was the only one, then he will get stuck on the plugin authorization screen: he can't add a new account and always sing in to previous account when click to sing in.

## Steps to Reproduce

1. git clone https://github.com/umbrellait-timur-khismatullin/google_sign_in_issue.git
2. run on iOS Simulator
3. tap to sign in
4. sing in with Google account
5. try to sign in again

Firebase configuration file added to the project. Auth mode set to internal.

<details>
 <summary>Logs</summary>
flutter run --verbose
https://pastebin.com/jkC80eUn

```
flutter analyze
Analyzing google_sign_in_issue...                                       
No issues found! (ran in 2.6s)
```

```
flutter doctor -v
[✓] Flutter (Channel stable, 3.0.2, on macOS 11.6 20G165 darwin-x64, locale ru-RU)
    • Flutter version 3.0.2 at /Users/timurkhismatullin/development/flutter
    • Upstream repository https://github.com/flutter/flutter.git
    • Framework revision cd41fdd495 (2 weeks ago), 2022-06-08 09:52:13 -0700
    • Engine revision f15f824b57
    • Dart version 2.17.3
    • DevTools version 2.12.2

[✓] Android toolchain - develop for Android devices (Android SDK version 30.0.3)
    • Android SDK at /Users/timurkhismatullin/Library/Android/sdk
    • Platform android-33, build-tools 30.0.3
    • Java binary at: /Applications/Android Studio.app/Contents/jre/Contents/Home/bin/java
    • Java version OpenJDK Runtime Environment (build 11.0.11+0-b60-7590822)
    • All Android licenses accepted.

[✓] Xcode - develop for iOS and macOS (Xcode 13.2.1)
    • Xcode at /Applications/Xcode.app/Contents/Developer
    • CocoaPods version 1.11.3

[✓] Chrome - develop for the web
    • Chrome at /Applications/Google Chrome.app/Contents/MacOS/Google Chrome

[✓] Android Studio (version 2020.3)
    • Android Studio at /Applications/Android Studio AF.app/Contents
    • Flutter plugin can be installed from:
      🔨 https://plugins.jetbrains.com/plugin/9212-flutter
    • Dart plugin can be installed from:
      🔨 https://plugins.jetbrains.com/plugin/6351-dart
    • Java version OpenJDK Runtime Environment (build 11.0.10+0-b96-7281165)

[✓] Android Studio (version 2021.1)
    • Android Studio at /Applications/Android Studio.app/Contents
    • Flutter plugin can be installed from:
      🔨 https://plugins.jetbrains.com/plugin/9212-flutter
    • Dart plugin can be installed from:
      🔨 https://plugins.jetbrains.com/plugin/6351-dart
    • Java version OpenJDK Runtime Environment (build 11.0.11+0-b60-7590822)

[✓] IntelliJ IDEA Community Edition (version 2021.2.1)
    • IntelliJ at /Applications/IntelliJ IDEA CE.app
    • Flutter plugin version 61.2.4
    • Dart plugin version 212.5080.8

[✓] VS Code (version 1.67.0)
    • VS Code at /Applications/Visual Studio Code.app/Contents
    • Flutter extension version 3.40.0

[✓] Connected device (4 available)
    • UmbrellaIT-iPhoneXR.white (mobile) • 00008020-000D04E00169002E            • ios            • iOS 14.8 18H17
    • iPhone 13 Pro Max (mobile)         • 11217F52-3E85-4AF7-A09A-2AC9052AFE92 • ios            • com.apple.CoreSimulator.SimRuntime.iOS-15-2 (simulator)
    • macOS (desktop)                    • macos                                • darwin-x64     • macOS 11.6 20G165 darwin-x64
    • Chrome (web)                       • chrome                               • web-javascript • Google Chrome 103.0.5060.53

[✓] HTTP Host Availability
    • All required HTTP hosts are available

• No issues found!
```

</details>



<details>
<summary>Video from original app</summary>

https://user-images.githubusercontent.com/84508364/175493781-a99cbd97-e0db-4aa1-b1bb-2151ea4f63ac.MP4

</details>