Separate reusable code from service-core.

The playback system is straightforward that it maps every note into its timestamps when
to start/stop playing. Included are the start and end indices when the notes are highlighted
in the data textarea.

Implement input in form.

Add integration tests and organize them by requirements.

Scaffold backend with Fastify CLI and replace Tap with Jest for
consistency.

The tests for each component has been set up. The way on writing tests
have been patterned from
https://kentcdodds.com/blog/common-mistakes-with-react-testing-library.

In addition, the requirements document has been modified to use a
consistent formatting which can be translated into code.

Add Web app package from Create Next App.