Flutter 3.7 + Firebase: Unable to establish connection on channel

I’m new to Flutter and Firebase and try to get a connection from a plain "flutter create test" project. Read a lot of tutorials but all seem to use Flutter2 but my project is using 3.7.7 and it seems not to work in the old way.

I created a public Firestore and got a Flutter2 tutorial app connecting, reading and writing. So it seems that Firestore is configured correctly.

I got google-services.json and put it in android/app directory.

In my test project I added these dependencies in pubspec.yaml`

  cloud_firestore: ^4.4.5
  firebase_core:

In main.dart I added

void main() async {
  WidgetsFlutterBinding.ensureInitialized();
  await Firebase.initializeApp();

  runApp(const MyApp());
}

When I try to run it I get this Exception:

PlatformException (PlatformException(channel-error, Unable to establish connection on channel., null, null))

So any further configuration needed? Or do I miss something else?