chore(core): Improve API documentation generation

[ermshiperete]

Currently we use hotdoc for generating the API documentation. However, the hotdoc_c_extension doesn't seem to be maintained anymore and isn't easy to install and work with hotdoc.

• Is there an alternate toolchain that supports c/c++ that we could use?
• or we could do the docs separate from the header

[ermshiperete]

Doxygen might be an alternative to hotdoc.

[srl295]

#10570