Repository: flutter
Issue: [google_sign_in] googleSignIn.signIn() return different account at first time and in second or third time on an account with multiple Youtube channels
Labels: p: google_sign_in,package,team-ecosystem,P2,triaged-ecosystem

Hello :)
I have a problem with Sign-in which is verified by @kevmoo.
I try to get my playlists from youtube after I sign-in with Google to my flutter app.
When I run my app on web at the first time everything is fine and I get my youtube data back.  Email is a little strange but as I say it works. Here is how email looks like.

```dart
final account = await _googleSignIn.signIn();
print(account?.email);
```

![Screenshot 2021-07-08 at 02 05 41](https://user-images.githubusercontent.com/44244477/124842992-348f7180-df91-11eb-9b5a-47001755dbcc.png)

But when I close the browser and run my app once again: flutter run -d chrome --web-port=1234
after click on sign in button I see poput with loader inside which close very fast (I can't choose my account) and now My account email  is:

![Screenshot 2021-07-08 at 02 14 02](https://user-images.githubusercontent.com/44244477/124843661-afa55780-df92-11eb-9fd7-455fc46cd864.png)

That's my real email

And I cant fetch any data from youtube because I get DetailedApiRequestError(status: 404, message: Channel not found.)

And Here is the full code if anyone want to check it:


<details> 
<summary>minimal code sample</summary> 

```dar
import 'package:extension_google_sign_in_as_googleapis_auth/extension_google_sign_in_as_googleapis_auth.dart'
    as auth;
import 'package:google_sign_in/google_sign_in.dart';
import 'package:googleapis/people/v1.dart';
import "package:googleapis/youtube/v3.dart";
import 'dart:async';
import 'package:flutter/material.dart';

void main() {
  runApp(
    MaterialApp(
      title: 'Google Sign In',
      home: SignInDemo(),
    ),
  );
}

class SignInDemo extends StatefulWidget {
  @override
  State createState() => SignInDemoState();
}

class SignInDemoState extends State<SignInDemo> {
  @override
  Widget build(BuildContext context) {
    return Scaffold(
        appBar: AppBar(
          title: const Text('Google Sign In'),
        ),
        body: ConstrainedBox(
          constraints: const BoxConstraints.expand(),
          child: _buildBody(),
        ));
  }

  Widget _buildBody() {
    return ElevatedButton(
      child: const Text('SIGN IN'),
      onPressed: _handleSignIn,
    );
  }

  Future<void> _handleSignIn() async {
    final _googleSignIn = new GoogleSignIn(
      scopes: [
        // PeopleServiceApi.contactsReadonlyScope,
        // YouTubeApi.youtubepartnerScope,
        // YouTubeApi.youtubeForceSslScope,
        // YouTubeApi.youtubeScope,
        YouTubeApi.youtubeReadonlyScope,
        // YouTubeApi.youtubeChannelMembershipsCreatorScope,
        // YouTubeApi.youtubeScope,
        // YouTubeApi.youtubepartnerChannelAuditScope,
      ],
    );
    await _googleSignIn.signOut();
    final account = await _googleSignIn.signIn();
    print(account?.email);
    print(account?.id);

    final httpClient = await _googleSignIn.authenticatedClient();
    final YouTubeApi youtubeApi = YouTubeApi((httpClient)!);

    final response = await youtubeApi.playlists.list(
      ["snippet"],
      mine: true,
      maxResults: 25,
    );
    print(response.items!.length);
    print(response.items);
  }
}
```

</details>