Repository: flutter
Issue: NavigationBar example issues with ScaffoldMessenger
Labels: framework,f: material design,d: examples,has reproducible steps,found in release: 3.3,found in release: 3.7,team-design,triaged-design

## Steps to Reproduce

Looking for a way to have persistent bottom navigation bar I came across the new NavigationBar with an example of how to do that. Unfortunatley this solution doesn't work with ScaffoldMessenger.

[https://github.com/flutter/flutter/blob/master/examples/api/lib/material/navigation_bar/navigation_bar.2.dart](https://github.com/flutter/flutter/blob/master/examples/api/lib/material/navigation_bar/navigation_bar.2.dart)

1. Execute `flutter run` on the code sample 
2. Tap FAB to show Snackbar and Banner.

**Expected results:** 
FAB moves up when snackbar is present.
Banner shows below app bar.   

**Actual results:** 
Snackbar covers FAB.
Banner shows above app bar.   

<details>
<summary>Code sample</summary>
Based on the example here.

```dart
// Copyright 2014 The Flutter Authors. All rights reserved.
// Use of this source code is governed by a BSD-style license that can be
// found in the LICENSE file.

/// Flutter code sample for [NavigationBar] with nested [Navigator] destinations.
import 'package:flutter/material.dart';

void main() {
  runApp(const MaterialApp(home: Home()));
}

class Home extends StatefulWidget {
  const Home({ super.key });

  @override
  State<Home> createState() => _HomeState();
}

class _HomeState extends State<Home> with TickerProviderStateMixin<Home> {
  static const List<Destination> allDestinations = <Destination>[
    Destination(0, 'Teal', Icons.home, Colors.teal),
    Destination(1, 'Cyan', Icons.business, Colors.cyan),
    Destination(2, 'Orange', Icons.school, Colors.orange),
    Destination(3, 'Blue', Icons.flight, Colors.blue),
  ];

  late final List<GlobalKey<NavigatorState>> navigatorKeys;
  late final List<GlobalKey> destinationKeys;
  late final List<AnimationController> destinationFaders;
  late final List<Widget> destinationViews;
  int selectedIndex = 0;

  AnimationController buildFaderController() {
    final AnimationController controller =  AnimationController(vsync: this, duration: const Duration(milliseconds: 200));
    controller.addStatusListener((AnimationStatus status) {
      if (status == AnimationStatus.dismissed) {
        setState(() { }); // Rebuild unselected destinations offstage.
      }
    });
    return controller;
  }

  @override
  void initState() {
    super.initState();
    navigatorKeys = List<GlobalKey<NavigatorState>>.generate(allDestinations.length, (int index) => GlobalKey()).toList();
    destinationFaders = List<AnimationController>.generate(allDestinations.length, (int index) => buildFaderController()).toList();
    destinationFaders[selectedIndex].value = 1.0;
    destinationViews = allDestinations.map((Destination destination) {
      return FadeTransition(
        opacity: destinationFaders[destination.index].drive(CurveTween(curve: Curves.fastOutSlowIn)),
        child: DestinationView(
          destination: destination,
          navigatorKey: navigatorKeys[destination.index],
        )
      );
    }).toList();
  }

  @override
  void dispose() {
    for (final AnimationController controller in destinationFaders) {
      controller.dispose();
    }
    super.dispose();
  }

  @override
  Widget build(BuildContext context) {
    return WillPopScope(
      onWillPop: () async {
        final NavigatorState navigator = navigatorKeys[selectedIndex].currentState!;
        if (!navigator.canPop()) {
          return true;
        }
        navigator.pop();
        return false;
      },
      child: Scaffold(
        body: SafeArea(
          top: false,
          child: Stack(
            fit: StackFit.expand,
            children: allDestinations.map((Destination destination) {
              final int index = destination.index;
              final Widget view = destinationViews[index];
              if (index == selectedIndex) {
                destinationFaders[index].forward();
                return Offstage(offstage: false, child: view);
              } else {
                destinationFaders[index].reverse();
                if (destinationFaders[index].isAnimating) {
                  return IgnorePointer(child: view);
                }
                return Offstage(child: view);
              }
            }).toList(),
          ),
        ),
        bottomNavigationBar: NavigationBar(
          selectedIndex: selectedIndex,
          onDestinationSelected: (int index) {
            setState(() {
              selectedIndex = index;
            });
          },
          destinations: allDestinations.map((Destination destination) {
            return NavigationDestination(
              icon: Icon(destination.icon, color: destination.color),
              label: destination.title,
            );
          }).toList(),
        ),
      ),
    );
  }
}

class Destination {
  const Destination(this.index, this.title, this.icon, this.color);
  final int index;
  final String title;
  final IconData icon;
  final MaterialColor color;
}

class RootPage extends StatelessWidget {
  const RootPage({ super.key, required this.destination });

  final Destination destination;

  Widget _buildDialog(BuildContext context) {
    return AlertDialog(
      title: Text('${destination.title} AlertDialog'),
      actions: <Widget>[
        TextButton(
          onPressed: () { Navigator.pop(context); },
          child: const Text('OK'),
        ),
      ],
    );
  }

  @override
  Widget build(BuildContext context) {
    final TextStyle headlineSmall = Theme.of(context).textTheme.headlineSmall!;
    final ButtonStyle buttonStyle = ElevatedButton.styleFrom(
      backgroundColor: destination.color,
      visualDensity: VisualDensity.comfortable,
      padding: const EdgeInsets.symmetric(vertical: 12, horizontal: 16),
      textStyle: headlineSmall,
    );

    return Scaffold(
      appBar: AppBar(
        title: Text('${destination.title} RootPage - /'),
        backgroundColor: destination.color,
      ),
      backgroundColor: destination.color[50],
      body: Center(
        child: Column(
          mainAxisSize: MainAxisSize.min,
          children: <Widget>[
            ElevatedButton(
              style: buttonStyle,
              onPressed: () {
                Navigator.pushNamed(context, '/list');
              },
              child: const Text('Push /list'),
            ),
            const SizedBox(height: 16),
            ElevatedButton(
              style: buttonStyle,
              onPressed: () {
                showDialog(
                  context: context,
                  useRootNavigator: false,
                  builder: _buildDialog,
                );
              },
              child: const Text('Local Dialog'),
            ),
            const SizedBox(height: 16),
            ElevatedButton(
              style: buttonStyle,
              onPressed: () {
                showDialog(
                  context: context,
                  useRootNavigator: true,
                  builder: _buildDialog,
                );
              },
              child: const Text('Root Dialog'),
            ),
            const SizedBox(height: 16),
            Builder(
              builder: (BuildContext context) {
                return ElevatedButton(
                  style: buttonStyle,
                  onPressed: () {
                    showBottomSheet(
                      context: context,
                      builder: (BuildContext context) {
                        return Container(
                          padding: const EdgeInsets.all(16),
                          width: double.infinity,
                          child: Text(
                            '${destination.title} BottomSheet\n'
                            'Tap the back button to dismiss',
                            style: headlineSmall,
                            softWrap: true,
                            textAlign: TextAlign.center,
                          ),
                        );
                      },
                    );
                  },
                  child: const Text('Local BottomSheet'),
                );
              },
            ),
          ],
        ),
      ),
      floatingActionButton: FloatingActionButton(
        child: const Icon(Icons.add),
        onPressed: () {
          ScaffoldMessenger.of(context)
              .showSnackBar(const SnackBar(content: Text('snackbar')));
          ScaffoldMessenger.of(context).showMaterialBanner(MaterialBanner(
            content: const Text('banner'),
            actions: [
              ElevatedButton(
                  onPressed: () {
                    ScaffoldMessenger.of(context).removeCurrentMaterialBanner();
                  },
                  child: const Text('close'))
            ],
          ));
        },
      ),
    );
  }
}

class ListPage extends StatelessWidget {
  const ListPage({ super.key, required this.destination });

  final Destination destination;

  @override
  Widget build(BuildContext context) {
    const int itemCount = 50;
    final ButtonStyle buttonStyle = OutlinedButton.styleFrom(
      foregroundColor: destination.color,
      fixedSize: const Size.fromHeight(128),
      textStyle: Theme.of(context).textTheme.headlineSmall,
    );
    return Scaffold(
      appBar: AppBar(
        title: Text('${destination.title} ListPage - /list'),
        backgroundColor: destination.color,
      ),
      backgroundColor: destination.color[50],
      body: SizedBox.expand(
        child: ListView.builder(
          itemCount: itemCount,
          itemBuilder: (BuildContext context, int index) {
            return Padding(
              padding: const EdgeInsets.symmetric(vertical: 4, horizontal: 8),
              child: OutlinedButton(
                style: buttonStyle.copyWith(
                  backgroundColor: MaterialStatePropertyAll<Color>(
                    Color.lerp(destination.color[100], Colors.white, index / itemCount)!
                  ),
                ),
                onPressed: () {
                  Navigator.pushNamed(context, '/text');
                },
                child: Text('Push /text [$index]'),
              ),
            );
          },
        ),
      ),
    );
  }
}

class TextPage extends StatefulWidget {
  const TextPage({ super.key, required this.destination });

  final Destination destination;

  @override
  State<TextPage> createState() => _TextPageState();
}

class _TextPageState extends State<TextPage> {
  late final TextEditingController textController;

  @override
  void initState() {
    super.initState();
    textController = TextEditingController(text: 'Sample Text');
  }

  @override
  void dispose() {
    textController.dispose();
    super.dispose();
  }

  @override
  Widget build(BuildContext context) {
    final ThemeData theme = Theme.of(context);
    return Scaffold(
      appBar: AppBar(
        title: Text('${widget.destination.title} TextPage - /list/text'),
        backgroundColor: widget.destination.color,
      ),
      backgroundColor: widget.destination.color[50],
      body: Container(
        padding: const EdgeInsets.all(32.0),
        alignment: Alignment.center,
        child: TextField(
          controller: textController,
          style: theme.primaryTextTheme.headlineMedium?.copyWith(
            color: widget.destination.color,
          ),
          decoration: InputDecoration(
            focusedBorder: UnderlineInputBorder(
              borderSide: BorderSide(
                color: widget.destination.color,
                width: 3.0,
              ),
            ),
          ),
        ),
      ),
    );
  }
}

class DestinationView extends StatefulWidget {
  const DestinationView({
    super.key,
    required this.destination,
    required this.navigatorKey,
  });

  final Destination destination;
  final Key navigatorKey;

  @override
  State<DestinationView> createState() => _DestinationViewState();
}

class _DestinationViewState extends State<DestinationView> {
  @override
  Widget build(BuildContext context) {
    return Navigator(
      key: widget.navigatorKey,
      onGenerateRoute: (RouteSettings settings) {
        return MaterialPageRoute<void>(
          settings: settings,
          builder: (BuildContext context) {
            switch(settings.name) {
              case '/':
                return RootPage(destination: widget.destination);
              case '/list':
                return ListPage(destination: widget.destination);
              case '/text':
                return TextPage(destination: widget.destination);
            }
            assert(false);
            return const SizedBox();
          },
        );
      },
    );
  }
}
```

</details>

<details>
  <summary>Logs</summary>
NA can reproduce in dart pad
</details>

<img src="https://user-images.githubusercontent.com/11432065/208039731-782c1b91-2f82-41c2-9b6d-6829becfe9f8.png" width="400">
Noticed I had snackbar as the title for the banner updated screenshot to code sample to avoid confusion.