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