Email verification in flutter with firebase doesnt work?

Question

I tried adding email verification logic in my flutter app with the help of firebase authentication. Now the issue I am facing is, that it works sending the verification mail via user.sendEmailVerification() , but the method user.emailVerified yeels false. And also the code which should be runned if the mail is verified doesnt run. The weird thing now is, that when I am File save the code in VS CODE (Strg + S), I am getting lead to the page where I should land when the email is verified (with the StreamBuilder in main.dart which checks if FirebaseAuth.instance.authStateChanges()): enter image description here I am trying to do it this way:

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

import '../screens/home_screen.dart';

class VerifyMailScreen extends StatefulWidget {
  final User _user;

  VerifyMailScreen(this._user);
  @override
  _VerifyMailScreenState createState() => _VerifyMailScreenState();
}

class _VerifyMailScreenState extends State<VerifyMailScreen> {
  final auth = FirebaseAuth.instance;
  Timer? timer;

  @override
  void initState() {
    super.initState();

    print(widget._user.email.toString());
    widget._user.sendEmailVerification();
    timer = Timer.periodic(Duration(seconds: 5), (timer) {
      _checkEmailVerified();
    });
  }

  Future<void> _checkEmailVerified() async {
    await widget._user.reload();
    if (widget._user.emailVerified) {
      timer!.cancel();
      Navigator.of(context).pushNamed(HomeScreen.routeName);
    }
    print(widget._user.email);
    print(widget._user.emailVerified);
  }

  @override
  void dispose() {
    super.dispose();
    timer!.cancel();
  }

  @override
  Widget build(BuildContext context) {
    return Scaffold(
      appBar: AppBar(
        centerTitle: true,
        actions: [
          IconButton(
              onPressed: () {
                auth.signOut();
              },
              icon: Icon(Icons.logout),
              color: Theme.of(context).textTheme.headline6!.color)
        ],
        title: Text(
          "Verify your mail",
          style: Theme.of(context).textTheme.headline6,
        ),
      ),
      body: Center(
        child: Column(
          crossAxisAlignment: CrossAxisAlignment.center,
          mainAxisAlignment: MainAxisAlignment.center,
          children: [
            Text("Verification screen"),
            ElevatedButton(
                onPressed: _checkEmailVerified, child: Text("Retry")),
          ],
        ),
      ),
    );
  }
}