Author of Material for MkDocs here. We're currently working on re-architecting the entire search engine and rewriting it from scratch. We're currently based on lunr.js, which is unmaintained as of 2020 and has more or less run its course. We've learned a lot what matters in respect to efficient and user friendly documentation search, and can't wait to give the first version into the hands of our users. I'm convinced that the next iteration of search we'll be releasing will solve many of the shortcomings that our current implementation has. Of course, it will work on the client side as it does now, no server needed, but there will be other options as well, e.g. for when your search index is in the megabytes and too big to ship to clients.