More sphinx builders

[LecrisUT]

This is a continuation of #2483 to discuss and track the other sphinx builders to add

• html: Already fully functional. Simplify the documentation building #2483 tracks the warnings as fatal errors
• linkcheck: In Add sphinx-builder linkcheck #2489
• man: Needs some consolidations on the hatch-scripts/makefile
• spellcheck: This is a difficult one, because PyEnchant does not seem to support full-word dictionaries, e.g. omni-present needs to be added as omni in the dictionary file. This builder needs more research if there are alternatives (original contributor switched to skyspell) (Omitted for now until a good alternative is found. codespell is helping a bit)
• doctest + shtest: Requires converting the rst files to the corresponding directives. No usage for doctest found so far

[LecrisUT]

For the spellcheck it seems @happz finds it usable in the current state, so I will deffer the implementation to them. I thought it didn't handle capitalization that well, e.g. CMake, but maybe there is a way of writing appropriate PyEnchant dictionary files for those. I would love to see that.