Improve the GitHub Action workflows

[fdiblen]

In #551 we made the first attempt to split and organize the GitHub Actions. Further improvements may be needed. GitHub documentation has a lot of useful recommendations and examples.

See: https://docs.github.com/en/actions/use-cases-and-examples/building-and-testing/building-and-testing-python

[carschno]

The setup-python action should use caching by default, see documentation:

steps:
- uses: actions/setup-python@v5
  with:
    cache: 'pip' # caching pip dependencies