I recently ported some docs to docusaurus, love it. Wish it had a builtin search indexer so it didn't need to jump out to another site for that.
Have you seen the community plugins - https://docusaurus.io/community/resources/#community-plugins. There are some search options there that may be of use to you.
Something in Docusaurus feels off. When you install it, you're not ready to go, there are a lot of things to clean and remove because it seems to be very tied to Facebook's use.
Maybe it's just me though.