ci: transition to jh-org typical release workflow

[consideRatio]

We have successfully started using PyPI's temporary credentials that can be granted from a GITHUB_TOKEN from a github workflow to make a release to PyPI assuming the project is pre-configured to trust a specific workflow in a github repository (release.yaml).

Should we transition to using that system in this project also perhaps? Then we can remove the PYPI_TOKEN github repository secret as well etc.

Action points

• [ ] Declare release.yaml as trusted via https://pypi.org/manage/project/batchspawner/settings/publishing/
• [ ] Do changes as made in this PR
• [ ] Cleanup PYPI_TOKEN from https://github.com/jupyterhub/batchspawner/settings/secrets/actions

Related org wide discussion

• https://github.com/jupyterhub/team-compass/issues/648