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.

The very link you posted says you can use the Node runtime, you're not limited to Edge runtime.