Primo is no ordinary static site, it uses Functions/Lambda/Workers to do things not possible in the Browser (these are little JavaScript files which get executed on every request). This is supported by Vercel, Netlify and Cloudflare (but with different usage limits, in my opinion cf has the highest). This is what you call dynamic websites. Primo needs Supabase to store information (so-called state) because each of these functions are stateless (they store no information).
To deploy Primo on Cloudflare, follow step 2 and 3, then create a new Cloudflare Pages project. Choose your desired Subdomain. In the next screen choose the SvelteKit Template. Now configure the Environment Variables under the Environment Variables Dropdown (the Video shows how to access them in Supabase). Now your project should be deployed normally like on Vercel.
If you have any other questions or issues, do not hesitate to ask. We'll help you!