Is anybody hooking up a keyboard and mouse to their ipad pro and using it as an interface to a remote desktop running in the cloud? If so, what software stack?

code-server https://github.com/coder/code-server works fairly well and can be saved to the home screen as a web applet to get rid of the browser URL bar. Their are a few UI issues related to touch but it has served well enough for some light work.

You can also use a remote apps like Rainway/TeamViewer/RDP/VNC somewhat successfully to get a more full desktop experience. Unfortunately they all seem to have their own input caveats that take some getting used to.

I am personally waiting for Parsec to release native iPadOS and tvOS clients as it provides the best experience I have found.

It seems like the gaming oriented remote desktop apps (Rainway https://rainway.com/, Parsec https://parsec.app/) are the best though as the latency on the more traditional ones is somewhat of a hindrance.

USB/Bluetooth keyboard and mouse support tends to work okay, but the simulated touch mouse makes getting used to things tough. If you have not tried using iPad OS with a mouse I suggest you look into before making a purchase as it is a fairly limiting experience.