Pagefind seems to be a great search tool for static (or SSRed) websites.

Pagefind is written in Rust and runs after my static site generator binary. pagefind indexes all generated HTML and provides an API to query that, including a search UI which you can see at the bottom of every page here. Perfect for my static site setup and it aims to not use much storage or bandwidth.

Available at https://pagefind.app/