Replace lychee

[ArBridgeman]

The hyperlink check with lychee is often failing:
https://github.com/exasol/ai-lab/actions/runs/23185303354/job/67367201073

In general, we should not be using external GitHub actions. While there are differences to this Python project & others, as it is already using a nox sessions, we could also add the Python Toolbox (>= 6.0.0) and use its hyperlink check.

[ArBridgeman]

There's a successor to lychee that would be more fitting due to the notebooks.

[tkilias]

If we want to use the PTB for checking the links in the documentation, we need to convert the documentation to sphinx.

[ckunki]

In PTB Nox session links:check calls _docs_list_links(), which calls sphinx-build -b linkcheck.