To clarify in the specific case of deploying to cloudflare workers, you can use cloudflares next-on-pages at the expense of a constrained "Edge" runtime.

- https://opennext.js.org/cloudflare#supported-nextjs-runtimes

You don't _need_ opennextjs to _not_ run on Vercel, but it does provide more flexibility than depending on Cloudflare alone (I don't know if there are any tradeoffs to consider as I haven't used it)

If you're new to this stack, I'd recommend taking some time with a toy app to get use to the architecture and frameworks, especially between running locally and deploying to a host. There are some differences that need to be aligned to get it working across all of them, especially when you introduce server actions.