1. A development experience with instant visual feedback for the frontend. Even more so when using tailwind.
2. A stable, safe and performant backend.
The downside is that a node process has to be running and doing the ssr, though that is an okay trade off for me because my project is mainly the api, having a reference implementation of the frontend is just a nice extra.
I've also experimented with implementing the reverse proxy in rust itself and using a unix socket and other IPC mechanisms to push the data to the SSR layer.
I think this most people would call this backend-, api- or service development. Especially if your api endpoint does not do anything web specific except http.
Anyway, how do you share types between the backend and frontend? Are you rawdogging json?
I use the ts-rs crate, which adds a derive(TS) macro for types in rust and generates typescript types. It works so far but my side projects are only medium sized. But I'm sure there are other options too.