Add an `index` to `DefaultTabController` to control active tab declaratively

### Steps to reproduce

this issue (https://github.com/flutter/flutter/issues/167169) is related but was closed

just run the following codesample

install latest riverpod and run it on android.

### Expected results

the tab visualization should show that the index has changed

### Actual results

When you press the button as in the video you can see that the tab will not change the index, although the value for initialIndex has changed

### Code sample

Code sample

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

void main() {
runApp(
ProviderScope(
child: DebugApp(),
),
);
}
class Counter extends Notifier {
@override
int build() => 0;
void increment() => state = (state + 1) % 2;
void set(int value) => state = value % 2;
}
final counter = NotifierProvider(Counter.new);
class DebugApp extends ConsumerWidget {
const DebugApp({super.key});

@override
Widget build(BuildContext context, WidgetRef ref) {
var index = ref.watch(counter);
return MaterialApp(
home: Material(
child: DefaultTabController(
length: 2,
initialIndex: index,
child: Column(
mainAxisAlignment: MainAxisAlignment.start,
crossAxisAlignment: CrossAxisAlignment.start,
children: [
TabBar(
tabs: List.generate(2, (i) =>
SizedBox(height: 100,width:100, child: Tab(child: Text("$i")))),
onTap: (index) => ref.read(counter.notifier).set(index),
),
OutlinedButton(
onPressed: ref
.read(counter.notifier)
.increment,
child: Text("Current Index $index",),
),
],
),
),
),
);
}
}
```

### Screenshots or Video

Screenshots / Video demonstration

[[Upload media here]](https://github.com/user-attachments/assets/f9e4a7fd-6e3b-418c-bdcd-7d06ff4070c5)

### Logs

Logs

```console
Syncing files to device SM G981B...
I/ViewRootImpl(18984): updatePointerIcon pointerType = 1000, calling pid = 18984
Restarted application in 1.241ms.
D/InputManager(18984): setPointerIconType iconId = 1000, callingPid = 18984
I/ViewRootImpl(18984): updatePointerIcon pointerType = 1000, calling pid = 18984
D/InputManager(18984): setPointerIconType iconId = 1000, callingPid = 18984
I/Choreographer(18984): Skipped 101 frames! The application may be doing too much work on its main thread.
I/ViewRootImpl(18984): updatePointerIcon pointerType = 1000, calling pid = 18984
D/InputManager(18984): setPointerIconType iconId = 1000, callingPid = 18984
I/ViewRootImpl(18984): updatePointerIcon pointerType = 1000, calling pid = 18984
D/InputManager(18984): setPointerIconType iconId = 1000, callingPid = 18984
```

### Flutter Doctor output

Doctor output

```console
Doctor summary (to see all details, run flutter doctor -v):
[√] Flutter (Channel stable, 3.38.5, on Microsoft Windows [Version 10.0.26200.7462], locale de-DE)
[√] Windows Version (11 Home 64-bit, 25H2, 2009)
[√] Android toolchain - develop for Android devices (Android SDK version 36.1.0-rc1)
[√] Chrome - develop for the web
[√] Visual Studio - develop Windows apps (Visual Studio Community 2022 17.14.14)
[√] Connected device (4 available)
! Device emulator-5562 is offline.
[√] Network resources

• No issues found!
```

Start with the provided main() reproduction and the related issue 167169, running the sample on Android to observe how changing initialIndex affects DefaultTabController. Trace the existing DefaultTabController behavior and decide how a declarative index should control the active tab; done means the displayed tab changes when the external index changes.

Written by the indexing model from the issue text.