Repository: flutter
Issue: [go_router] Back button not appearing when using Shellroute
Labels: package,has reproducible steps,P3,p: go_router,team-go_router,triaged-go_router,found in release: 3.19,found in release: 3.21

### What package does this bug report belong to?

go_router

### What target platforms are you seeing this bug on?

Android

### Have you already upgraded your packages?

Yes

### Dependency versions

<details><summary>pubspec.lock</summary>

```lock
# Generated by pub
# See https://dart.dev/tools/pub/glossary#lockfile
packages:
  async:
    dependency: transitive
    description:
      name: async
      sha256: "947bfcf187f74dbc5e146c9eb9c0f10c9f8b30743e341481c1e2ed3ecc18c20c"
      url: "https://pub.dev"
    source: hosted
    version: "2.11.0"
  boolean_selector:
    dependency: transitive
    description:
      name: boolean_selector
      sha256: "6cfb5af12253eaf2b368f07bacc5a80d1301a071c73360d746b7f2e32d762c66"
      url: "https://pub.dev"
    source: hosted
    version: "2.1.1"
  characters:
    dependency: transitive
    description:
      name: characters
      sha256: "04a925763edad70e8443c99234dc3328f442e811f1d8fd1a72f1c8ad0f69a605"
      url: "https://pub.dev"
    source: hosted
    version: "1.3.0"
  clock:
    dependency: transitive
    description:
      name: clock
      sha256: cb6d7f03e1de671e34607e909a7213e31d7752be4fb66a86d29fe1eb14bfb5cf
      url: "https://pub.dev"
    source: hosted
    version: "1.1.1"
  collection:
    dependency: transitive
    description:
      name: collection
      sha256: ee67cb0715911d28db6bf4af1026078bd6f0128b07a5f66fb2ed94ec6783c09a
      url: "https://pub.dev"
    source: hosted
    version: "1.18.0"
  cupertino_icons:
    dependency: "direct main"
    description:
      name: cupertino_icons
      sha256: d57953e10f9f8327ce64a508a355f0b1ec902193f66288e8cb5070e7c47eeb2d
      url: "https://pub.dev"
    source: hosted
    version: "1.0.6"
  fake_async:
    dependency: transitive
    description:
      name: fake_async
      sha256: "511392330127add0b769b75a987850d136345d9227c6b94c96a04cf4a391bf78"
      url: "https://pub.dev"
    source: hosted
    version: "1.3.1"
  flutter:
    dependency: "direct main"
    description: flutter
    source: sdk
    version: "0.0.0"
  flutter_lints:
    dependency: "direct dev"
    description:
      name: flutter_lints
      sha256: a25a15ebbdfc33ab1cd26c63a6ee519df92338a9c10f122adda92938253bef04
      url: "https://pub.dev"
    source: hosted
    version: "2.0.3"
  flutter_test:
    dependency: "direct dev"
    description: flutter
    source: sdk
    version: "0.0.0"
  flutter_web_plugins:
    dependency: transitive
    description: flutter
    source: sdk
    version: "0.0.0"
  go_router:
    dependency: "direct main"
    description:
      name: go_router
      sha256: "170c46e237d6eb0e6e9f0e8b3f56101e14fb64f787016e42edd74c39cf8b176a"
      url: "https://pub.dev"
    source: hosted
    version: "13.2.0"
  lints:
    dependency: transitive
    description:
      name: lints
      sha256: "0a217c6c989d21039f1498c3ed9f3ed71b354e69873f13a8dfc3c9fe76f1b452"
      url: "https://pub.dev"
    source: hosted
    version: "2.1.1"
  logging:
    dependency: transitive
    description:
      name: logging
      sha256: "623a88c9594aa774443aa3eb2d41807a48486b5613e67599fb4c41c0ad47c340"
      url: "https://pub.dev"
    source: hosted
    version: "1.2.0"
  matcher:
    dependency: transitive
    description:
      name: matcher
      sha256: "1803e76e6653768d64ed8ff2e1e67bea3ad4b923eb5c56a295c3e634bad5960e"
      url: "https://pub.dev"
    source: hosted
    version: "0.12.16"
  material_color_utilities:
    dependency: transitive
    description:
      name: material_color_utilities
      sha256: "9528f2f296073ff54cb9fee677df673ace1218163c3bc7628093e7eed5203d41"
      url: "https://pub.dev"
    source: hosted
    version: "0.5.0"
  meta:
    dependency: transitive
    description:
      name: meta
      sha256: a6e590c838b18133bb482a2745ad77c5bb7715fb0451209e1a7567d416678b8e
      url: "https://pub.dev"
    source: hosted
    version: "1.10.0"
  path:
    dependency: transitive
    description:
      name: path
      sha256: "8829d8a55c13fc0e37127c29fedf290c102f4e40ae94ada574091fe0ff96c917"
      url: "https://pub.dev"
    source: hosted
    version: "1.8.3"
  sky_engine:
    dependency: transitive
    description: flutter
    source: sdk
    version: "0.0.99"
  source_span:
    dependency: transitive
    description:
      name: source_span
      sha256: "53e943d4206a5e30df338fd4c6e7a077e02254531b138a15aec3bd143c1a8b3c"
      url: "https://pub.dev"
    source: hosted
    version: "1.10.0"
  stack_trace:
    dependency: transitive
    description:
      name: stack_trace
      sha256: "73713990125a6d93122541237550ee3352a2d84baad52d375a4cad2eb9b7ce0b"
      url: "https://pub.dev"
    source: hosted
    version: "1.11.1"
  stream_channel:
    dependency: transitive
    description:
      name: stream_channel
      sha256: ba2aa5d8cc609d96bbb2899c28934f9e1af5cddbd60a827822ea467161eb54e7
      url: "https://pub.dev"
    source: hosted
    version: "2.1.2"
  string_scanner:
    dependency: transitive
    description:
      name: string_scanner
      sha256: "556692adab6cfa87322a115640c11f13cb77b3f076ddcc5d6ae3c20242bedcde"
      url: "https://pub.dev"
    source: hosted
    version: "1.2.0"
  term_glyph:
    dependency: transitive
    description:
      name: term_glyph
      sha256: a29248a84fbb7c79282b40b8c72a1209db169a2e0542bce341da992fe1bc7e84
      url: "https://pub.dev"
    source: hosted
    version: "1.2.1"
  test_api:
    dependency: transitive
    description:
      name: test_api
      sha256: "5c2f730018264d276c20e4f1503fd1308dfbbae39ec8ee63c5236311ac06954b"
      url: "https://pub.dev"
    source: hosted
    version: "0.6.1"
  vector_math:
    dependency: transitive
    description:
      name: vector_math
      sha256: "80b3257d1492ce4d091729e3a67a60407d227c27241d6927be0130c98e741803"
      url: "https://pub.dev"
    source: hosted
    version: "2.1.4"
  web:
    dependency: transitive
    description:
      name: web
      sha256: afe077240a270dcfd2aafe77602b4113645af95d0ad31128cc02bce5ac5d5152
      url: "https://pub.dev"
    source: hosted
    version: "0.3.0"
sdks:
  dart: ">=3.2.2 <4.0.0"
  flutter: ">=3.13.0"

```
</details>


### Steps to reproduce

1.Create a ShellRoute with some routes.
2.From these GoRoutes provide Scaffold Widgets.
3.Use the push() method to navigate to these Routes.

Hint: Providing a Scaffold inside the ShellRoute builder method, to wrap the actual child, results in a working back button! See the example code for both cases.

### Expected results

Expect a Scaffold widget provided by a GoRoute within a ShellRoute to show the back button correctly.

### Actual results
A Scaffold widget provided by a GoRoute within a ShellRoute does not show the back button correctly.

### Code sample

<details open><summary>Code sample</summary>

```dart
import 'package:flutter/material.dart';
import 'package:go_router/go_router.dart';

void main() {
  runApp(const MyApp());
}

class MyApp extends StatelessWidget {
  const MyApp({super.key});

  // This widget is the root of your application.
  @override
  Widget build(BuildContext context) {
    return MaterialApp.router(
      title: 'Flutter Demo',
      theme: ThemeData(
        colorScheme: ColorScheme.fromSeed(seedColor: Colors.deepPurple),
        useMaterial3: true,
      ),
      routerConfig: RouterStuff.router,
    );
  }
}

class RouterStuff {
  static GlobalKey<NavigatorState> _rootNavigatorKey = GlobalKey<NavigatorState>(debugLabel: "root");
  static GlobalKey<NavigatorState> _branchNavigatorKey = GlobalKey<NavigatorState>(debugLabel: "branch");
  static GlobalKey<NavigatorState> _branchNavigatorKey2 = GlobalKey<NavigatorState>(debugLabel: "branch2");

  static GoRouter router = GoRouter(
    initialLocation: "/a",
    navigatorKey: _rootNavigatorKey,
    routes: <RouteBase>[
      StatefulShellRoute.indexedStack(
        branches: [
          StatefulShellBranch(navigatorKey: _branchNavigatorKey, routes: [
            GoRoute(path: "/a", builder: (context, state) => PageA()),
            ShellRoute(
                builder: (context, state, child) {
                  return child;
                },
                routes: [
                  GoRoute(path: "/b", builder: (context, state) => PageB()),
                ]),
            ShellRoute(
              builder: (context, state, child) {
                return Scaffold(
                  appBar: AppBar(
                    title: Text("Back Button Works"),
                  ),
                  body: child,
                );
              },
              routes: [
                GoRoute(path: "/c", builder: (context, state) => PageC()),
              ],
            )
          ]),
          StatefulShellBranch(navigatorKey: _branchNavigatorKey2, routes: [
            GoRoute(path: "/foo", builder: (context, state) => PageB()),
          ])
        ],
        builder: (context, state, shell) => Scaffold(
          body: shell,
        ),
      ),
    ],
  );
}

class PageA extends StatelessWidget {
  const PageA({super.key});

  @override
  Widget build(BuildContext context) {
    return Scaffold(
      appBar: AppBar(),
      body: Container(
        width: double.infinity,
        child: Column(
          crossAxisAlignment: CrossAxisAlignment.center,
          mainAxisAlignment: MainAxisAlignment.center,
          children: [
            FilledButton(
              onPressed: () => GoRouter.of(context).push("/b"),
              child: Text("Go To B"),
            ),
            FilledButton(
              onPressed: () => GoRouter.of(context).push("/c"),
              child: Text("Go To C"),
            ),
          ],
        ),
      ),
    );
  }
}

class PageC extends StatelessWidget {
  const PageC({super.key});

  @override
  Widget build(BuildContext context) {
    return Center(
      child: Text("Page C"),
    );
  }
}

class PageB extends StatelessWidget {
  const PageB({super.key});

  @override
  Widget build(BuildContext context) {
    return Scaffold(
      appBar: AppBar(
        title: Text("no back button!"),
      ),
      body: Center(
        child: Text("Page B"),
      ),
    );
  }
}

```

</details>


### Screenshots or Videos

<details open>
<summary>Screenshots / Video demonstration</summary>

[Upload media here]

</details>


### Logs

_No response_

### Flutter Doctor output

<details open><summary>Doctor output</summary>

```console
Doctor summary (to see all details, run flutter doctor -v):
[✓] Flutter (Channel stable, 3.16.2, on macOS 14.2.1 23C71 darwin-arm64, locale en-CH)
[✓] Android toolchain - develop for Android devices (Android SDK version 34.0.0)
[✓] Xcode - develop for iOS and macOS (Xcode 15.3)
[✓] Chrome - develop for the web
[✓] Android Studio (version 2023.1)
[✓] VS Code (version 1.87.0)
[✓] Connected device (4 available)
[✓] Network resources

• No issues found!
```

</details>