Minimal code :

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

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

class MyApp extends StatelessWidget {
  MyApp({super.key});

  final GoRouter _router = GoRouter(
    initialLocation: '/page1',
    routes: [
      ShellRoute(
        builder: (context, state, child) {
          return ScaffoldWithNavRail(child: child);
        },
        routes: [
          GoRoute(
            path: '/page1',
            builder: (context, state) => const PageWithPopupMenu(title: 'Page 1'),
          ),
          GoRoute(
            path: '/page2',
            builder: (context, state) => const PageWithPopupMenu(title: 'Page 2'),
          ),
        ],
      ),
    ],
  );

  @override
  Widget build(BuildContext context) {
    return MaterialApp.router(
      routerConfig: _router,
      title: 'Flutter Demo',
      theme: ThemeData(
        colorScheme: ColorScheme.fromSeed(seedColor: Colors.deepPurple),
        useMaterial3: true,
      ),
    );
  }
}

class ScaffoldWithNavRail extends StatelessWidget {
  final Widget child;

  const ScaffoldWithNavRail({required this.child, super.key});

  @override
  Widget build(BuildContext context) {
    return Scaffold(
      body: Row(
        children: <Widget>[
          NavigationRail(
            selectedIndex: _getSelectedIndex(context),
            onDestinationSelected: (int index) {
              _onDestinationSelected(context, index);
            },
            labelType: NavigationRailLabelType.selected,
            destinations: const <NavigationRailDestination>[
              NavigationRailDestination(
                icon: Icon(Icons.looks_one),
                selectedIcon: Icon(Icons.looks_one),
                label: Text('Page 1'),
              ),
              NavigationRailDestination(
                icon: Icon(Icons.looks_two),
                selectedIcon: Icon(Icons.looks_two),
                label: Text('Page 2'),
              ),
            ],
          ),
          const VerticalDivider(thickness: 1, width: 1),
          Expanded(child: child),
        ],
      ),
    );
  }

  int _getSelectedIndex(BuildContext context) {
    final String location = '/page1';
    switch (location) {
      case '/page1':
        return 0;
      case '/page2':
        return 1;
      default:
        return 0;
    }
  }

  void _onDestinationSelected(BuildContext context, int index) {
    switch (index) {
      case 0:
        context.go('/page1');
        break;
      case 1:
        context.go('/page2');
        break;
    }
  }
}

class PageWithPopupMenu extends StatelessWidget {
  final String title;

  const PageWithPopupMenu({required this.title, super.key});

  @override
  Widget build(BuildContext context) {
    return Scaffold(
      appBar: AppBar(
        title: Text(title),
      ),
      body: PopupMenuButton<String>(
        icon: Icon(Icons.more_vert),
        onSelected: (String result) {
          ScaffoldMessenger.of(context).showSnackBar(
            SnackBar(content: Text('Selected: $result')),
          );
        },
        itemBuilder: (BuildContext context) => <PopupMenuEntry<String>>[
          const PopupMenuItem<String>(
            value: 'Item 1',
            child: Text('Item 1'),
          ),
          const PopupMenuItem<String>(
            value: 'Item 2',
            child: Text('Item 2'),
          ),
          const PopupMenuItem<String>(
            value: 'Item 3',
            child: Text('Item 3'),
          ),
        ],
      ),
    );
  }
}

So now start the code. Click the dropdown menu. Normally, when you click anywhere outside of the drop-down menu, it closes(its cancelled and oncanceled is called). But here clicks from the NavigationRail() are listened to.When U click on navigation icons .oncanCanlled() isnt called. I want when I click the navigationRail, the dropdown menu is closed and onCanceled() is called and not that I navigate.

Hint: In this example, the program seems to work with a small problem. But in my big app, the DropDwonMenu is kept hanging without its buttons and is not disposed when I navigate.I

Image of how the popupmenu is still hanging in my code :enter image description here.