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

I use Hugo Book[1] for the documentation of FormBeep[2]

It's been super easy and I host it free on CF pages:

[1]https://hugo-book-demo.netlify.app/docs/example/ [2]https://docs.formbeep.com

I have used this one : https://deepsite.hf.co/

It generates static pages using only HTML and CSS, which makes it blazing fast. It can also handle jQuery and JavaScript very smoothly.

https://www.11ty.dev/ ?

"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")

Nikola https://getnikola.com