Flutter Provider and Navigator

so This is my first try with Flutter. I come from Angular where dependency injection made routing a breeze. Just injecting the Router to any service would just do the trick. Here is my scenario for flutter app:

In '/login' page I click Login button. This calls method from Auth provider, where after validating credentials Application should be routed to '/home'.

It's just something I can't wrap my head around even though I read all possible threads in the freaking internet. Everybody said one shoud wrap MaterialApp with ChangeNotifierProvider which I did - what am I doing wrong?

Here is my code. Can you point me to the right direction?

import 'package:flutter/material.dart';
import 'package:provider/provider.dart';

void main() {
  runApp(MyApp());
}

class MyApp extends StatelessWidget {
  @override
  Widget build(BuildContext context) {
    return ChangeNotifierProvider(
      create: (_) => Auth(context: context),
      child: MaterialApp(
        initialRoute: "/login",
        routes: {
          "/login": (context) => LoginPage(),
          "/home": (context) => HomePage()
        },
      ),
    );
  }
}

//This is my Login page Widget - After successful login I want to be able to use Navigator to push to '/home' route
class LoginPage extends StatelessWidget {
  @override
  @override
  Widget build(BuildContext context) {
    return Scaffold(
        appBar: AppBar(
          title: Text("Login"),
        ),
        body: ElevatedButton(
          //
          onPressed: () => {
            // here I want to use login method on Auth provider. Which should validate credentials and if valid redirect to home page
            Provider.of<Auth>(context, listen: false).login()
          },
          child: Text("login"),
        ));
  }
}

//This is my Home page Widget
class HomePage extends StatelessWidget {
  @override
  Widget build(BuildContext context) {
    return Container(
      child: Scaffold(appBar: AppBar(title: Text("Home"))),
    );
  }
}

//This is my auth controller where After successful login I want to redirect to HomePage

class Auth extends ChangeNotifier {
  BuildContext context;
  Auth({
    required this.context,
  });

  // This is login method of Auth provider -
  login() {
    //Here after validating the credentials (eg user / password) I want to redirect to '/home' route.
    Navigator.of(context).pushNamed("/home");
  }
}