Search options for “static” site

I currently have are personal WordPress blog and I’m looking to migrate it to a static site but keep WordPress on the backend – using Simply Static to export the static page, it’s working well.

The one thing I’m missing in terms of functionality from the standard WordPress site is search.

I’ve been trying to get a Google Programmable Search working, but my “test” site has been up for a week and the configured Programmable Search doesn’t return anything no matter what I search for.

I think the best option is going to be something like Lunr.js or meilisearch.com (but that would still need to be hosted somewhere, and my goal in moving to a static site was to not run the server).

Any ideas?

Thanks