I use and recommend Lume [1] for static site generation, and I know it has a couple of search plugins, but I haven't used them. As others have mentioned, your search without JS requirement will be hard to implement, unless you use an external provider for the indexing and search.

[1] https://lume.land

How are you expecting search to work without JS? I'm pretty sure you would need either some sort of backend OR JS for any sort of search to work.

Or maybe another option would be to outsource the search part to "site:yourdomain" on google or something similar.

I’m using middleman for ages and been pretty happy with it. It’s a ruby-based static side generator framework.

I have no idea about speed. Markdown support sure, I use HAML as well. There are search plugins but you can use any a publicly available search engine (Google, DuckDuckGo, etc) for that if you want to avoid JS or backend DBs.

"Search without JS" and "static site generation" doesn't make much sense. Without client-side search, you'll need a search product or back-end search functionality? (both of which are not "static")

There are some static sites that provide simple searches, but they require javascript.

You could use something like mintlify to do this. Im on their free plan and it gets the job done