snowee Here is my idea, do you think it will work?
get a 27" 4K monitor
continue with Budgie, set resolution for desktop usage to 1920 x 1200 (this is my current screen res)
before gaming, set resolution to 4K
immediately start up Steam
play games on Steam at 4K resolution

I would not mess with screen resolution because the results will not be satisfactory (fuzziness and so on).

I would work with fractional scaling instead, changing the scaling back and forth between normal use and games.

At 4K resolution, Budgie offers 100%/200%/300%. One of those settings is likely to be satisfactory for running Budgie for normal purposes on a 4K monitor, although it might not be identical to running Budgie at 1920x1080.

As a lifelong mentor used to remind me, "Life is a game of inches." Running Budgie on a 4K monitor, you might never get to "perfect", but you will probably get to "good enough".

I think you will like 4K, no matter what the scaling, because the screens tend to be very clear because of the high number of pixels. The next time you are in a computer store, look at an Apple laptop running Retina or a Dell XPS running a high-resolution screen. Both are scaled significantly, but the displays are gorgeous even so. That's what you will likely get running Budgie at 200% or 300% on a 4k monitor. You just might have to get used to a slightly different screen layout.

      tomscharbach although it might not be identical to running Budgie at 1920x1080

      It might be quite close. Our 55" 4K TV sits about 12' away from our chairs in the living room, and I use Plasma at 325% scaling for the media computer. To me, it appears to be very much like to viewing similar content on my laptop that's on a stand in front of my chair. 300% on Budgie could work very well.