One thing shared between old software rendered desktops and modern videogames is that they shunned these intermediate 'composited' screens. On the desktop, there used to be the screen, and basically windows used to draw on top of each other, there was no intermediate buffer for the whole window to draw itself to, which would then be smushed together with all others.

Video games are the same (mostly) - everything is rendered in screen space for performance reasons, it's very, very rare, that you would render something into a temporary buffer then composite it on top of the rest of the scene - you would need exceptional reasons for that.

Maybe it's time to get back to the olden days of display servers - where applications would push a list of render commands to the 'display server', which would consist of rendering primitives, which would then take these commands and construct the whole UI on the screen, without the intermediate steps of each app drawing into its own little buffer.

You could always fall back to drawing your own applciations, then asking the display server to composite that, but that would pretty much be the exception, not the norm.