You can absolutely host the entirety of your React code on a CDN - in fact, that's the preferred way of doing it. Node is used locally to generate the static resources needed by your app. There is also the server-side rendering approach enabled by frameworks such as Next.js - those indeed run on the server and provide a way of merging frontend and backend development.

To be honest, if jQuery has worked for you so far, it's not clear to me you need to be switching. It's possible your requirements just don't have enough frontend complexity to make the change worthwhile. I'd suggest working through the excellent React docs and building something very simple. If it clicks - great! If not, you haven't committed yourself to support tech you don't need. Either way, greenfield is better, don't jump into retrofitting an existing jQuery codebase.