• Closes Improve doctesting #588

The idea is to use sphinx.ext.doctest to be able to run examples and check their output.
I think we tried that a very long time ago, but we had two issues:

• We had some tests that failed due to float numerical errors on some different system. This is less likely to happen now that the value tests of aggregators have moved from doc tests to unit tests (test_values.py). We can also try as much as we can to not have unstable numerical results in the documentation.
• We couldn't emphasize lines with the doctest directives. Claude has been quite useful this time by extending the directive and adding the emphasize-lines option to it. A more long-term solution would be to contribute this change directly to the sphinx repo, by fixing Add :caption: for .. doctest:: sphinx-doc/sphinx#6915 and testcode directives should support the same options as code-block sphinx-doc/sphinx#6858. But for now, it works.
• We relied on doc tests to reach 100% code coverage if I remember correctly. This is not the case anymore (we have 100% without doc tests).

In a future step, I'd like to try to also test the examples from the README. I think we could import the entire README to some other place (like the main page of torchjd.org, to avoid having to maintain one). Then, it could be doctested when we run uv run make doctest -C docs. So this would solve two problems at once. But this is out of the scope of this PR, as the README examples were never tested.

Changes:

• Fix output errors in documentation examples
• Add sphinx.ext.doctest extension
• Add emphasize-lines to testcode. This also adds the docutils doc dependency.
• Remove pytest doc tests
• Add testcode directives for doctests
• Update instructions on doc testing
• Move lightning from test to doc deps
• Update checks so that the build-doc job runs doctest

TODO before merging: change expected check from "Build documentation" to "Build and test documentation" in ruleset.