You can open desktop mode inside of gamemode, just like any other game or application. I find it easier to use most desktop apps this way instead of adding them individually to steam.
To do this, download this script. Save it as a script and make the script executable. Finally right click the file and “add to steam”.
Some important notes with this: You can’t exit steam while running the desktop this way, so apps that require closing steam (like steam rom manager) won’t work. There are also a few apps that do weird things, like cryoutilities shows up super tiny this way. But generally most everything works.
Script seems fine to me. But good on you for being skeptical about running random scripts.
Given that SteamOS isn’t a particularly private/secure OS I’m not running anything with personal info on it anyway so it’s not really a huge concern. And yeah as you say the script looks fine, just calling stuff that’s already there rather than reaching out to the internet or installing anything new!