I wouldn't do that if you have the hardware to keep things separated but it's because of what I run on my server. You need to take into consideration that besides CPU/GPU usage a server's heavy load will be on Network and Disks, so while the system looks like it's not doing much, it might be doing a lot of Io operations. The thing with that is that both your disks and your network have a limited capacity, so if you're trying to play a game you might get longer load screens and higher ping that you would with one machine for each.

That being said it vastly depends on what you're running on the server, but higher pings and lower fps are a given since now you'll have more processes running on the background, so for games that are CPU bottlenecked it will be a massive hit.

I did something like this some years ago now. I had watched the “One PC, 2 Screens” (or something like that) From Linus Tech Tips, so I wanted to try it myself.

Using Unraid makes it easy to setup and I had 2 Windows VMs with their own screen and keyboard/mouse, dedicated GPU and then docker running my selfhosted stuff.

It uses more power though, because the PC is always on and the hardware needs to be beefy.

VMware workstation works great. Just install Windows or linux on the box, workstation, and fire up all the VMs you could dream of, while using the PC as a normal PC.

But just know that any time you need to reboot your PC PC you need to reboot your server, which sucks. It's much better to just keep the old office PC. That old i5 uses so little power at idle vs a modern CPU being perpetually kept awake.