My brain hasn’t woken up yet today.
What a great idea! Why have I never thought of that?!
I think you can find the folder where your steam screenshots are, and with the location in mind, go to your desktop, right click, look for personalise or similar, then you can set the wallpaper to be from a folder.
So set the location to be your steam folder.
steam_install_location\userdata\your_steam_id\760\remote
(I think the 760 will be the same for everyone…)
Inside there are folders, one for each game named with the game’s Steam ID. There’s probably some other bits in there depending on game, but also probably a screenshot folder.
So for example, for me and American Truck Simulator
C:\Games\Steam\userdata\X\760\remote\270880\screenshots
X is my Steam ID, 270880 is the Steam ID of ATS.
(I actually do a silly thing where save games, screenshots, and other things I might want to preserve but games scatter all over depending on the developer. I replace the folders with symbolic links to a common location. So all my screenshots and save games actually end up in the place. Makes backups easier, too. The magic is done via an elevated command prompt and the command mklink /d.)