It depends on what you're doing. I have some flows that execute console apps (DOS EXE's) that run in the background, as well as flows that execute API calls. If you have one that needs to interface with a browser or standard application, those will need to run in the foreground. That said, I'm able to run some browser flows in a browser on one display while I do other things in the other display. This could glitch if I needed to do keyboard entry in my flow, but I don't.
I've also been trying to run flows in a VM, with mixed results. In theory if you could run a flow on a VM, you may be able to just minimize the VM window and the flow will still execute.
Browsers have the ability to run "headless", which means don't actually have a display but pretend you do. Some tools take advantage of this (Jenkins comes to mind) but Power Automate does not.