Yes I plan on adding doc search. Although I'm not sure if I should try to build one from scratch (never tried building full text search before) or using something prebuilt like Algolia docsearch.

Algolia docsearch would host an AI view of the doc, on its own website with its own stack, no?

It resembles deepwiki (which I used on several of my projects, see for example https://deepwiki.com/pthom/imgui_bundle).

If algolia is close to deepwiki as I suspect, that does not replace the original doc site: it needs to index an existing doc site before. So adding (even a simple) search to this site would be worth it imho.

No I think that's a different product. What I had in mind is what is on, for example, https://tailwindcss.com/ and many other open source project websites. If you open the search menu, you'll see at the bottom that it's powered by Algolia docsearch.

Basically its a service that automatically crawls your docs and creates a search index and widget that you can include on your website.