[jokerttu]

Migrates the example app to package:material_ui, following the official migration guide. The plugin's own requirements are unchanged.

• example/pubspec.yaml requires sdk: ^3.13.0 and flutter: ">=3.47.0", the environment material_ui declares, and adds material_ui: ^1.10.0.
• Imports were rewritten with dart fix --apply --code=migrate_design_widgets. The example uses no Cupertino library and no localization delegates, so nothing else needed migrating.
• Dart 3.13 rejects final on a function parameter; one parameter in navigation.dart drops it.
• A separate commit applies the Dart 3.13 formatter to the example, since the language version change restyles it. It contains formatting only.

CI

• All jobs move from Flutter 3.44.x to 3.47.x, because melos resolves the example in every job and the example now needs 3.47.
• A new job, Run Dart analysis and unit tests on minimum Flutter, keeps checking the plugin on 3.44.x, the minimum in the root pubspec.yaml. It runs flutter pub get --no-example, flutter analyze --no-pub lib test --fatal-infos and flutter test --no-pub. Native unit tests and builds now run on 3.47.x only.

Stacked on #794.

Checks run

• Flutter 3.47.9: flutter analyze . --fatal-infos clean in the plugin and the example, dart format reports no changes, 268 Dart tests pass.
• Flutter 3.44.9: the minimum-Flutter job's three steps pass locally.
• Workflow YAML parses.
• Not yet run with this change: example builds and Patrol integration tests on Android and iOS. A full run on both platforms will follow on the top of the stack.

Map taps on iOS with Flutter 3.47. Flutter 3.47's iOS engine asks PlatformDispatcher.onHitTest whether a touch belongs to a platform view, and blocks the touch when no callback answers. GestureBinding installs that callback, but flutter_test's TestPlatformDispatcher doesn't forward it to the real dispatcher, so under Patrol every tap on the map was blocked, and both t06 "Test map UI settings" variants failed. The patrol() wrapper in patrol_test/shared.dart now installs the same answer GestureBinding gives in an app. Apps aren't affected; this only changes the test binding. With it, t06_map_test.dart passes 12/12 on the iOS 26.5 simulator with Flutter 3.47.9.

Pre-launch Checklist

• I read the Contributor Guide and followed the process outlined there for submitting PRs.
• I signed the CLA.
• I listed at least one issue that this PR fixes in the description above.
• I updated/added relevant documentation
• I added new tests to check the change I am making
• All existing and new tests are passing.