Add ability to maintain bottom view padding in NavigationBar safe area (#162076)

Fixes [When the on-screen keyboard is open, NavigationBar does not
maintainBottomViewPadding in Edge-to-Edge
mode](https://github.com/flutter/flutter/issues/159526)

### Description 

According to the
[SafeArea.maintainBottomViewPadding](https://api.flutter.dev/flutter/widgets/SafeArea/maintainBottomViewPadding.html)
docs, it is expected that `NavigationBar` will shift when the view
padding changes. This PR provides ability to override the
`maintainBottomViewPadding` property in the under `SafeArea` in the
`NavigationBar`.


### Code Sample

<details>
<summary>expand to view the code sample</summary> 

```dart
import 'package:flutter/material.dart';
import 'package:flutter/services.dart';

void main() async {
  WidgetsFlutterBinding.ensureInitialized();

  await SystemChrome.setEnabledSystemUIMode(SystemUiMode.edgeToEdge);

  runApp(const MyApp());
}

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

  @override
  Widget build(BuildContext context) {
    return MaterialApp(
      debugShowCheckedModeBanner: false,
      home: Scaffold(
        appBar: AppBar(
          title: const Text('Sample'),
        ),
        body: const Center(
          child: Padding(
            padding: EdgeInsets.all(16.0),
            child: TextField(
              decoration: InputDecoration(border: OutlineInputBorder()),
            ),
          ),
        ),
        bottomNavigationBar: NavigationBar(
          maintainBottomViewPadding: true,
          destinations: const <Widget>[
          NavigationDestination(icon: Icon(Icons.favorite_rounded), label: 'Favorite'),
          NavigationDestination(icon: Icon(Icons.favorite_rounded), label: 'Favorite'),
          NavigationDestination(icon: Icon(Icons.favorite_rounded), label: 'Favorite')
        ]),
        floatingActionButton: FloatingActionButton(
          onPressed: () {},
          child: const Icon(Icons.add),
        ),
      ),
    );
  }
}
```

</details>

### With `maintainBottomViewPadding: false` (Default)



https://github.com/user-attachments/assets/1cea27d4-2d6d-4bca-bb9a-53c0a21fdb4d


### With `maintainBottomViewPadding: true`



https://github.com/user-attachments/assets/b6c7487f-e23c-43db-a365-90bf69fa03dd



## Pre-launch Checklist

- [x] I read the [Contributor Guide] and followed the process outlined
there for submitting PRs.
- [x] I read the [Tree Hygiene] wiki page, which explains my
responsibilities.
- [x] I read and followed the [Flutter Style Guide], including [Features
we expect every widget to implement].
- [x] I signed the [CLA].
- [x] I listed at least one issue that this PR fixes in the description
above.
- [x] I updated/added relevant documentation (doc comments with `///`).
- [x] I added new tests to check the change I am making, or this PR is
[test-exempt].
- [ ] I followed the [breaking change policy] and added [Data Driven
Fixes] where supported.
- [x] All existing and new tests are passing.

If you need help, consider asking for advice on the #hackers-new channel
on [Discord].

<!-- Links -->
[Contributor Guide]:
https://github.com/flutter/flutter/blob/main/docs/contributing/Tree-hygiene.md#overview
[Tree Hygiene]:
https://github.com/flutter/flutter/blob/main/docs/contributing/Tree-hygiene.md
[test-exempt]:
https://github.com/flutter/flutter/blob/main/docs/contributing/Tree-hygiene.md#tests
[Flutter Style Guide]:
https://github.com/flutter/flutter/blob/main/docs/contributing/Style-guide-for-Flutter-repo.md
[Features we expect every widget to implement]:
https://github.com/flutter/flutter/blob/main/docs/contributing/Style-guide-for-Flutter-repo.md#features-we-expect-every-widget-to-implement
[CLA]: https://cla.developers.google.com/
[flutter/tests]: https://github.com/flutter/tests
[breaking change policy]:
https://github.com/flutter/flutter/blob/main/docs/contributing/Tree-hygiene.md#handling-breaking-changes
[Discord]:
https://github.com/flutter/flutter/blob/main/docs/contributing/Chat.md
[Data Driven Fixes]:
https://github.com/flutter/flutter/blob/main/docs/contributing/Data-driven-Fixes.md

packages/flutter/lib/src/material/navigation_bar.dart

@@ -2,6 +2,7 @@
 // Use of this source code is governed by a BSD-style license that can be
 // found in the LICENSE file.
 
+/// @docImport 'package:flutter/services.dart';
 /// @docImport 'bottom_navigation_bar.dart';
 /// @docImport 'navigation_rail.dart';
 /// @docImport 'scaffold.dart';
@@ -113,6 +114,7 @@ class NavigationBar extends StatelessWidget {
     this.overlayColor,
     this.labelTextStyle,
     this.labelPadding,
+    this.maintainBottomViewPadding = false,
   }) : assert(destinations.length >= 2),
        assert(0 <= selectedIndex && selectedIndex < destinations.length);
 
@@ -245,6 +247,24 @@ class NavigationBar extends StatelessWidget {
   /// the top.
   final EdgeInsetsGeometry? labelPadding;
 
+  /// Specifies whether the underlying [SafeArea] should maintain the bottom
+  /// [MediaQueryData.viewPadding] instead of the bottom [MediaQueryData.padding].
+  ///
+  /// When true, this will prevent the [NavigationBar] from shifting when opening a
+  /// software keyboard due to the change in the padding value, especially when the
+  /// app uses [SystemUiMode.edgeToEdge], which renders the system bars over the
+  /// application instead of outside it.
+  ///
+  /// Defaults to false.
+  ///
+  /// See also:
+  ///
+  ///  * [SafeArea.maintainBottomViewPadding], which specifies whether the [SafeArea]
+  ///    should maintain the bottom [MediaQueryData.viewPadding].
+  ///  * [SystemUiMode.edgeToEdge], which sets a fullscreen display with status and
+  ///    navigation elements rendered over the application.
+  final bool maintainBottomViewPadding;
+
   VoidCallback _handleTap(int index) {
     return onDestinationSelected != null ? () => onDestinationSelected!(index) : () {};
   }
@@ -265,6 +285,7 @@ class NavigationBar extends StatelessWidget {
       surfaceTintColor:
           surfaceTintColor ?? navigationBarTheme.surfaceTintColor ?? defaults.surfaceTintColor,
       child: SafeArea(
+        maintainBottomViewPadding: maintainBottomViewPadding,
         child: SizedBox(
           height: effectiveHeight,
           child: Row(

packages/flutter/test/material/navigation_bar_test.dart

@@ -1600,6 +1600,37 @@ void main() {
     expect(_getLabelStyle(tester, disabledText).fontSize, equals(disabledTextStyle.fontSize));
     expect(_getLabelStyle(tester, disabledText).color, equals(disabledTextStyle.color));
   });
+
+  testWidgets('NavigationBar.maintainBottomViewPadding can consume bottom MediaQuery.padding', (
+    WidgetTester tester,
+  ) async {
+    const double bottomPadding = 40;
+    const TextDirection textDirection = TextDirection.ltr;
+
+    await tester.pumpWidget(
+      MaterialApp(
+        home: Directionality(
+          textDirection: textDirection,
+          child: MediaQuery(
+            data: const MediaQueryData(padding: EdgeInsets.only(bottom: bottomPadding)),
+            child: Scaffold(
+              bottomNavigationBar: NavigationBar(
+                maintainBottomViewPadding: true,
+                destinations: const <Widget>[
+                  NavigationDestination(icon: Icon(Icons.ac_unit), label: 'AC'),
+                  NavigationDestination(icon: Icon(Icons.access_alarm), label: 'Alarm'),
+                ],
+              ),
+            ),
+          ),
+        ),
+      ),
+    );
+
+    final double safeAreaBottomPadding =
+        tester.widget<Padding>(find.byType(Padding).first).padding.resolve(textDirection).bottom;
+    expect(safeAreaBottomPadding, equals(0));
+  });
 }
 
 Widget _buildWidget(Widget child, {bool? useMaterial3}) {