I am not able to go to landing page after google sign in in flutter

Question

I am trying to implement a google sign for my application using firebase. when i press on google sign in button a pop up window appear to select the mail id when i press on my mail id i am not redirecting to LoggedInWidgit() page. I am not getting where my code is not working

home_page.dart

import 'package:flutter/material.dart';
import 'package:firebase_auth/firebase_auth.dart';
import 'package:note_app_demo/screens/login_page.dart';
import 'package:note_app_demo/utilities/logged_in_widgit.dart';

class HomePage extends StatelessWidget {
  const HomePage({Key? key}) : super(key: key);

  @override
  Widget build(BuildContext context) => Scaffold(
        body: StreamBuilder(
          stream: FirebaseAuth.instance.authStateChanges(),
          builder: (context, snapshot) {
            if (snapshot.connectionState == ConnectionState.waiting) {
              return Center(
                child: CircularProgressIndicator(),
              );
            } else if (snapshot.hasData) {
              return LogedInWidgit();
            } else if (snapshot.hasError) {
              return Center(
                child: Text('Something went Wrong!'),
              );
            } else {
              return LOGIN_PAGE();
            }
          },
        ),
      );
}

logged_in_widgit.dart

import 'package:flutter/material.dart';
import 'package:note_app_demo/utilities/scaffold.dart';
import 'package:firebase_auth/firebase_auth.dart';

class LogedInWidgit extends StatelessWidget {
  const LogedInWidgit({Key? key}) : super(key: key);

  @override
  Widget build(BuildContext context) {
    final user = FirebaseAuth.instance.currentUser!;
    return Scaffold(
      appBar: AppBar(
        title: Text('Logged In'),
        centerTitle: true,
        actions: [
          TextButton(
            onPressed: () {},
            child: Text('Logout'),
          )
        ],
      ),
      body: Container(
        alignment: Alignment.center,
        color: Colors.blueGrey.shade900,
        child: Column(
          children: [
            Text(
              'Profile',
              style: TextStyle(fontSize: 24),
            ),
            SizedBox(
              height: 32,
            ),
            CircleAvatar(
              radius: 40,
              backgroundImage: NetworkImage(user.photoURL!),
            ),
            SizedBox(
              height: 8,
            ),
            Text(
              'Name: ' + user.displayName!,
              style: TextStyle(color: Colors.white, fontSize: 16),
            ),
            SizedBox(
              height: 8,
            )
          ],
        ),
      ),
    );
  }
}

main.dart

import 'package:firebase_auth/firebase_auth.dart';
import 'package:flutter/material.dart';
import 'package:note_app_demo/provider/google_sign_in.dart';
import 'package:note_app_demo/screens/landing_page.dart';
import 'package:flutter/services.dart';
import 'package:note_app_demo/screens/login_page.dart';
import 'package:firebase_core/firebase_core.dart';
import 'package:provider/provider.dart';

void main() async {
  WidgetsFlutterBinding.ensureInitialized();
  SystemChrome.setPreferredOrientations(
      [DeviceOrientation.portraitUp, DeviceOrientation.portraitDown]);
  await Firebase.initializeApp();
  runApp(const MyApp());
}

class MyApp extends StatelessWidget {
  const MyApp({Key? key}) : super(key: key);

  @override
  Widget build(BuildContext context) => ChangeNotifierProvider(
        create: (context) => GoogleSignInProvider(),
        child: MaterialApp(
          debugShowCheckedModeBanner: false,
          title: 'Studiac',
          home: LOGIN_PAGE(),
        ),
      );
}

login_page.dart

import 'package:flutter/material.dart';
import 'package:font_awesome_flutter/font_awesome_flutter.dart';
import 'package:note_app_demo/provider/google_sign_in.dart';
import 'package:note_app_demo/screens/landing_page.dart';
import 'package:note_app_demo/button.dart';
import 'package:font_awesome_flutter/font_awesome_flutter.dart';
import 'package:provider/provider.dart';

class LOGIN_PAGE extends StatelessWidget {
  const LOGIN_PAGE({Key? key}) : super(key: key);

  @override
  Widget build(BuildContext context) {
    return SafeArea(
      child: Scaffold(
        body: SafeArea(
          child: Column(
            mainAxisAlignment: MainAxisAlignment.center,
            children: [
              Padding(
                padding: const EdgeInsets.all(10.0),
                child: ElevatedButton.icon(
                  icon: FaIcon(
                    Icons.email,
                    color: Colors.blue,
                  ),
                  label: Text('Sign Up with Email'),
                  onPressed: () {},
                  style: ElevatedButton.styleFrom(
                    primary: Colors.tealAccent,
                    onPrimary: Colors.black,
                    minimumSize: Size(double.infinity, 50),
                  ),
                ),
              ),
              Padding(
                padding: const EdgeInsets.all(10.0),
                child: ElevatedButton.icon(
                  icon: FaIcon(
                    FontAwesomeIcons.google,
                    color: Colors.red,
                  ),
                  label: Text('Sign Up with Google'),
                  onPressed: () {
                    final provider = Provider.of<GoogleSignInProvider>(context,
                        listen: false);
                    provider.googleLogin();
                  },
                  style: ElevatedButton.styleFrom(
                    primary: Colors.tealAccent,
                    onPrimary: Colors.black,
                    minimumSize: Size(double.infinity, 50),
                  ),
                ),
              ),
            ],
          ),
        ),
      ),
    );
  }
}

google_sign_in.dart

import 'package:flutter/material.dart';
import 'package:google_sign_in/google_sign_in.dart';
import 'package:firebase_auth/firebase_auth.dart';

class GoogleSignInProvider extends ChangeNotifier {
  final googleSignIn = GoogleSignIn();
  GoogleSignInAccount? _user;

  //getter to get google sign in
  GoogleSignInAccount get user => _user!;
  Future googleLogin() async {
    try {
      final googleUser = await googleSignIn.signIn();
      if (googleUser == null) return;
      _user = googleUser;
      final googleAuth = await googleUser.authentication;
      final credential = GoogleAuthProvider.credential(
          accessToken: googleAuth.accessToken, idToken: googleAuth.idToken);
      await FirebaseAuth.instance.signInWithCredential(credential);
    } catch (e) {
      print(e.toString());
    }
    notifyListeners();
  }

  Future logout() async {
    await googleSignIn.disconnect();
    FirebaseAuth.instance.signOut();
  }
}