Cloudflare Pages has a configurable option to disable automatic production branch deployments without disabling automatic branch previews for non-production branches/PRs. For a recent site I deployed, this feature was a requirement, so we had to deploy it on Cloudflare (I would have otherwise used Netlify for this site).
Apologies, this feature already exists and is called “Locked Deploys” (see Manage deploys | Netlify Docs).
I was originally looking for this feature under the Site configuration → Build & deploy → Build Settings but the only toggle there is Build Status (Active or Stopped) which appears to control both production and deploy previews.
To disable only the production deploys, you have open a previous production deploy and click the “Lock to stop auto publishing” option on that deploy.