True, I tested this out to check something earlier and noted Firefox using the GPU, even though at 0% whilst minimised, the allocation was there inc VRAM:
Whilst minimised, VRAM was reading allocated at 1.4GB for the entire system inc Firefox. Closing Firefox resulted in 0.6GB VRAM allocated for the entire system, so DWM isn't really a factor in this scenario on Windows 11 22H2 at least. Keep in mind that on 22H2 Windows will suspend background processes as long as they comply with the UWP/Power status groups - So effectively many apps could be completely suspended by Windows 11 if they comply with those requirements for Windows to be able to do that. You will see yellow/green icons under the Status column in task manager showing what apps were suspended to improve performance.
Normally when I game I never close Firefox down purely because at this res and all max settings I only see 9GB of VRAM use in RTSS, that's %process% use so only the game using up to 9GB VRAM, so if I had 1.4GB VRAM being used by the rest of the system inc minimised Firefox, then I'd still be under the 12GB of my card.
realistically I would want at least 16GB on my next card because games will get bigger, but I am also keeping an eye on what happens with DirectStorage/RTXIO. There'd be less strain on VRAM if textures are streaming direct to the GPU in realtime going forwards so having to worry about system VRAM use etc should not be a worry if future games are making use of this API I think.