More sphinx builders

[LecrisUT]

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

• [x] html: Already fully functional. #2483 tracks the warnings as fatal errors
• [ ] linkcheck: In #2489
• [ ] man: Needs some consolidations on the hatch-scripts/makefile
• [x] ~~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