main.dart

class _MainPageState extends State<MainPage> with SingleTickerProviderStateMixin {
  ...
    
  void _restart() {
    setState(() {
      hasStarted = false;
      isPlaying = true;
      notes = initNotes();
      points = 0;
      currentNoteIndex = 0;
    });
    animationController.reset();
  }

  void _showFinishDialog() {
    showDialog(
      ...
    ).then((_) => _restart()); //<-- restart game when dialog is closed
  }
}