Root predictive back (https://github.com/flutter/flutter/pull/120385) was reverted in https://github.com/flutter/flutter/pull/132167.  This PR is an attempt to reland it.

The reversion happened due to failed Google tests (b/295073110).

Breaking google testing 
revert of: https://github.com/flutter/flutter/pull/120385
b/295065534

This PR aims to support Android's predictive back gesture when popping the entire Flutter app.  Predictive route transitions between routes inside of a Flutter app will come later.

<img width="200" src="https://user-images.githubusercontent.com/389558/217918109-945febaa-9086-41cc-a476-1a189c7831d8.gif" />

### Trying it out

If you want to try this feature yourself, here are the necessary steps:

  1. Run Android 33 or above.
  1. Enable the feature flag for predictive back on the device under "Developer
     options".
  1. Create a Flutter project, or clone [my example project](https://github.com/justinmc/flutter_predictive_back_examples).
  1. Set `android:enableOnBackInvokedCallback="true"` in
     android/app/src/main/AndroidManifest.xml (already done in the example project).
  1. Check out this branch.
  1. Run the app. Perform a back gesture (swipe from the left side of the
     screen).

You should see the predictive back animation like in the animation above and be able to commit or cancel it.

### go_router support

go_router works with predictive back out of the box because it uses a Navigator internally that dispatches NavigationNotifications!

~~go_router can be supported by adding a listener to the router and updating SystemNavigator.setFrameworkHandlesBack.~~

Similar to with nested Navigators, nested go_routers is supported by using a PopScope widget.

<details>

<summary>Full example of nested go_routers</summary>

```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.

import 'package:go_router/go_router.dart';

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

void main() => runApp(_MyApp());

class _MyApp extends StatelessWidget {
  final GoRouter router = GoRouter(
    routes: <RouteBase>[
      GoRoute(
        path: '/',
        builder: (BuildContext context, GoRouterState state) => _HomePage(),
      ),
      GoRoute(
        path: '/nested_navigators',
        builder: (BuildContext context, GoRouterState state) => _NestedGoRoutersPage(),
      ),
    ],
  );

  @override
  Widget build(BuildContext context) {
    return MaterialApp.router(
      routerConfig: router,
    );
  }
}

class _HomePage extends StatelessWidget {
  @override
  Widget build(BuildContext context) {
    return Scaffold(
      appBar: AppBar(
        title: const Text('Nested Navigators Example'),
      ),
      body: Center(
        child: Column(
          mainAxisAlignment: MainAxisAlignment.center,
          children: <Widget>[
            const Text('Home Page'),
            const Text('A system back gesture here will exit the app.'),
            const SizedBox(height: 20.0),
            ListTile(
              title: const Text('Nested go_router route'),
              subtitle: const Text('This route has another go_router in addition to the one used with MaterialApp above.'),
              onTap: () {
                context.push('/nested_navigators');
              },
            ),
          ],
        ),
      ),
    );
  }
}

class _NestedGoRoutersPage extends StatefulWidget {
  @override
  State<_NestedGoRoutersPage> createState() => _NestedGoRoutersPageState();
}

class _NestedGoRoutersPageState extends State<_NestedGoRoutersPage> {
  late final GoRouter _router;
  final GlobalKey<NavigatorState> _nestedNavigatorKey = GlobalKey<NavigatorState>();

  // If the nested navigator has routes that can be popped, then we want to
  // block the root navigator from handling the pop so that the nested navigator
  // can handle it instead.
  bool get _popEnabled {
    // canPop will throw an error if called before build. Is this the best way
    // to avoid that?
    return _nestedNavigatorKey.currentState == null ? true : !_router.canPop();
  }

  void _onRouterChanged() {
    // Here the _router reports the location correctly, but canPop is still out
    // of date.  Hence the post frame callback.
    SchedulerBinding.instance.addPostFrameCallback((Duration duration) {
      setState(() {});
    });
  }

  @override
  void initState() {
    super.initState();

    final BuildContext rootContext = context;
    _router = GoRouter(
      navigatorKey: _nestedNavigatorKey,
      routes: [
        GoRoute(
          path: '/',
          builder: (BuildContext context, GoRouterState state) => _LinksPage(
            title: 'Nested once - home route',
            backgroundColor: Colors.indigo,
            onBack: () {
              rootContext.pop();
            },
            buttons: <Widget>[
              TextButton(
                onPressed: () {
                  context.push('/two');
                },
                child: const Text('Go to another route in this nested Navigator'),
              ),
            ],
          ),
        ),
        GoRoute(
          path: '/two',
          builder: (BuildContext context, GoRouterState state) => _LinksPage(
            backgroundColor: Colors.indigo.withBlue(255),
            title: 'Nested once - page two',
          ),
        ),
      ],
    );

    _router.addListener(_onRouterChanged);
  }

  @override
  void dispose() {
    _router.removeListener(_onRouterChanged);
    super.dispose();
  }

  @override
  Widget build(BuildContext context) {
    return PopScope(
      popEnabled: _popEnabled,
      onPopped: (bool success) {
        if (success) {
          return;
        }
        _router.pop();
      },
      child: Router<Object>.withConfig(
        restorationScopeId: 'router-2',
        config: _router,
      ),
    );
  }
}

class _LinksPage extends StatelessWidget {
  const _LinksPage ({
    required this.backgroundColor,
    this.buttons = const <Widget>[],
    this.onBack,
    required this.title,
  });

  final Color backgroundColor;
  final List<Widget> buttons;
  final VoidCallback? onBack;
  final String title;

  @override
  Widget build(BuildContext context) {
    return Scaffold(
      backgroundColor: backgroundColor,
      body: Center(
        child: Column(
          mainAxisAlignment: MainAxisAlignment.center,
          children: <Widget>[
            Text(title),
            //const Text('A system back here will go back to Nested Navigators Page One'),
            ...buttons,
            TextButton(
              onPressed: onBack ?? () {
                context.pop();
              },
              child: const Text('Go back'),
            ),
          ],
        ),
      ),
    );
  }
}
```

</details>

### Resources

Fixes https://github.com/flutter/flutter/issues/109513
Depends on engine PR https://github.com/flutter/engine/pull/39208  
Design doc: https://docs.google.com/document/d/1BGCWy1_LRrXEB6qeqTAKlk-U2CZlKJ5xI97g45U7azk/edit#
Migration guide: https://github.com/flutter/website/pull/8952

I get confused when reading this comment. It seems that this code never calls `AnimationController.fling` (but only things like `animateTo`). Therefore, I do not think discussing the duration of `AnimationController.fling` is helpful - maybe it is just an outdated comment?

Sync lints with https://github.com/dart-lang/linter/blob/master/example/all.yaml and enable `implicit_reopen` and `type_literal_in_constant_pattern` (which have no violations). Also contains some clean-up work towards enabling `matching_super_parameters`, which is not quite ready yet due to its handling of "private" arguments.

Update `CupertinoPageRoute` transition animation curves

Remove 1745 decorative breaks

* Use `curly_braces_in_flow_control_structures` for `animation`

* Use `curly_braces_in_flow_control_structures` for `cupertino`

* fix comments

Revert "Add ability for `ModalRoutes` to ignore pointers during transitions and do so on `Cupertino` routes (#95757)" (#104520)

This reverts commit 4c0b0be2.

Add ability for `ModalRoutes` to ignore pointers during transitions and do so on `Cupertino` routes (#95757)

Improve iOS fidelity of `barrierColor`s and edge decorations for full-screen Cupertino page transitions (#95537)

This does a cleanup of the examples, removing all of the "section" markers and extra comments that we don't need anymore now that the samples are no longer in the source code. It also removes the --template arguments from the {@tool dartpad} and {@tool sample} directives, since those are no longer used. It converts two examples that I discovered were still embedded into linked examples in the examples folder.

I didn't delete the templates from the snippets config folder yet, because there are still embedded samples in the dart:ui package from the engine that use them. Once dart:ui no longer uses the templates, they can be removed.

I bumped the version of the snippets package to pick up a change that allows removal of the --template argument.

This extracts the sample code out from the API doc comments, and places them in separate files on disk, allowing running of the examples locally, testing them, and building of slightly larger examples.

* Create state restoration templates, 

* Update existing state restoration samples to use the new templates

* Add to README, decided to require stateful widgets to include RestorationMixin

Update samples to use repo analysis options, Fix sample templates and a ton of analyzer issues (#77868)

* Expose CupertinoModalPopupRoute for state restoration

* Add state restoration test, expose kCupertinoModalBarrierColor

Adds Navigator.maybeOf to replace calling Navigator.of(context, nullOk: true), and removes the nullOk parameter. Also changes Navigator.of to return a non-nullable value, and removes many (120!) instances of the ! operator, reducing the possible places where a null dereference could occur.

* Remove nullOk from cupertino color resolution

* Add CupertinoDynamicColor.maybeResolveFrom

* Remove CupertinoDynamicColor.maybeResolveFrom again