Update app-cutter after 2.0 release

(Jason: @danielhollas I use this issue to track the things require to do to make this cutter more friendly and more fit with current infrastructures we have now, hope you don't mind).

- [ ] ~~(TBD) using [`copier`](https://copier.readthedocs.io/en/stable/) which is using jinja like a template and [gets along well with `ruff` lint](https://github.com/astral-sh/ruff/issues/5824).~~
- [ ] Drop `setup.py` which not needed anymore with `aiidalab>=23.3.2`
- [ ] Use new notebook test framework used in AWB by installing app and loading notebook on the `full-stack` container.
- [x] Docs template using `mkdocs` as the backend.