Every time I'm in Desktop Mode this pops up. It seems to be spawned by Steam Proton, though I'm not sure why since it happens even before I launch a game or software. Can't figure out what exact process is running it. Hitting install either fails checksum, or nothing happens after it finishes the download, and then it just pops up again. Any ideas?
Open system monitor and inspect processes tobsee where doest it come from. You can also open terminal and type
ps -aux | grep -i wine
That should yeild some more info including full command line of Wine's processes.
The pop up however runs always if Wine prefix doesn't have Mono implementation installed.
It can be Steam trying to perform some task while updating a game, but without additional info it's hard to tell
Sorry for the late reply. I haven't had time to try this 'til this morning. The results are that while I haven't gotten the issue fixed, I at least know what's happening now.
So what's happening is similar to what you said. I have an older Custom Proton installed for some picky games, and its included Mono install is old. Desktop Steam doesn't seem to like this for some reason and keeps trying to update the Mono installed, but this keeps failing for some reason. I tried messing with it but haven't figured out a solution yet. I'll have to try more things later.
I don't know about Steam/Proton trying to install Mono itself, but Wine definitely does that (and Proton is just Wine with extras and scripts)
At that point, I'd just locate which game it is and rename its directory in compatdata then removed the old one atfer confirming that it's fixed. If the game doesn't support cloud saves, you might want to find and move your progress to the new prefix.