https://www.superstreamsystem.com/ might be what you are looking for, you can set up scenes and overlays etc

Only ones I know of are aimed at mobile streamers eg https://www.obs-server.com/obs-server/

However you can run obs and stream from pretty much any of the cloud gaming services that provide a full system eg shadow.tech, paperspace

I'm curious what you mean by this, like a service that would handle the encoding?

(Disclaimer: I have no idea what the point of a streaming PC is)