Bunny has just that. They just call it edge storage and you can use it as origin.
Sounds like you'd be happier using Workers Sites, which has been available for over a year. https://blog.cloudflare.com/workers-sites/
The point of Cloudflare Pages is to provide the CI for you, which some people want. If you don't want that, then keep using Workers Sites.
The link in that blog redirects to this new service.
Yeah, I guess it's assumed that most users probably want to use Cloudflare Pages instead. But Workers Sites still exists as a feature in `wrangler`, the Cloudflare Workers CLI tool.
Workers Sites itself is really just some automation for uploading files into Workers KV, along with a template Worker script that serves them as a static site. You could build your own from scratch if you wanted.
My point here is that the low-level tools are readily available if that's what you want. You don't have to use Cloudflare Pages if you'd rather have more control.
(I am the tech lead for Cloudflare Workers...)
https://developers.cloudflare.com/pages/platform/build-confi...
I currently use Netlify as it has a simple API to deploy a zip file or a slightly more complicated API to avoid re-uploading unchanged files if you have a big site.
https://docs.netlify.com/api/get-started/#deploy-via-api
I'm glad that Cloudflare is adding the option to be an origin for static sites, I would switch over if they added the option to just upload files to them without this CI/CD nonsense.