Recreate `example` project

[nivisi]

The example project was created 3 years ago. It will soon no longer be launchable. Flutter already throws a warning and disallows to run the project:

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Warning
──────────────────────────────────────────────────────────────────────────────
Your Flutter application is created using an older version of the Android
embedding. It is being deprecated in favor of Android embedding v2. Follow the
steps at
https://flutter.dev/go/android-project-migration
to migrate your project. You may also pass the --ignore-deprecation flag to
ignore this check and continue with the deprecated v1 embedding. However,
the v1 Android embedding will be removed in future versions of Flutter.
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...
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Build failed due to use of deprecated Android v1 embedding.
Exited (1)