Migrate example to Android embedding v2

[nilsreichardt]

Description

The example of this package isn't migrated to Android embedding v2 yet.

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Warning
──────────────────────────────────────────────────────────────────────────────
Your Flutter application is created using an older version of the Android
embedding. It's being deprecated in favor of Android embedding v2. Follow the
steps at

https://flutter.dev/go/android-project-migration

to migrate your project.

Steps to reproduce

1. Open example
2. Run flutter pub get

[jakobleck]

Check out https://github.com/jakobleck/flutter_app_badger/commit/57d55389bf42c7853e0243ed60387aae407dbf98 Tested with Flutter 3.10.5 and three different devices/emulators running Android 11, 13 and 14. Example app starts on Android, but badge count update does not work, getting an error as in https://github.com/leolin310148/ShortcutBadger/issues/90, no good prospect considering the maintenance status of ShortcutBadger...