I'm running a Common Lisp webserver with (I believe) nginx in front. It's fairly low maintenance, but it is dynamic web content (the entire point is to generate names on request), so I unless the CDN has some sort of function interface, I don't see how that would work.
If you can rewrite that part of it as a JS function, you can probably host it as a free or very very cheap serverless function on Cloudflare or Vercel. Either would also be able to host the static parts of your site for free or very cheap.
Vercel is a AWS and other cloud whitelabeler. Cloudflare has their own networks.
Yeah, the static portion is trivial. The trouble with the dynamic portion is that I use a proprietary C/C++ library that I'd have to replace. I suppose in this day and age I ought to be able to do better with some of the modern deep learning techniques that are available, but I haven't been able to invest the effort to figure that out yet.