It does. With proton, each game runs in its own “prefix” (basically like a fake C:/ drive) which is where the launcher is installed. When you uninstall a game, the prefix gets deleted as well (it didn’t used to)
GTA V’s prefix should be located under .steam/root/steamapps/compatdata/271590/pfx/
if you want to check for it (make sure “Show hidden files” is enabled in the file manager)
Search for “Nested Desktop” in the start menu and right-click it/add to Steam. Then return to game mode and run it.
This lets you launch the desktop as an app in game mode, so it should keep the same color settings.
Use one of the community layouts for controls