[Updated] Steam client bugged update indicator after switching between desktop and game mode

[This is an updated version of a post I made yesterday and incorrectly believed to be fixed]

A weird bug with Steam on bazzite-gnome-deck (running the latest stable 40.20240427.0) on a Steam Deck LCD. Sometimes in game mode, Steam will report that a Steam client update is available. Suspiciously, however, this update will "install" instantaneously, and the update indicator will later appear again. At first I thought the pattern was random, but after a few days of this, it looks like the bugged update indicator comes back when switching between game mode and desktop mode.

Yesterday when I was trying to debug this, someone suggested I check the steam stdout output to see if there's any clues there. Indeed, you can see in my attached .steam-stdout.log Steam seems to believe an update is available, and "installs" it suspiciously quickly looking at the timestamps. But nothing seems to pop out as a possible problem, other than the fact that it claims I am opted in to a client beta when I am not (message is Opted in to client beta 'steamdeck_stable' via beta file not sure if this is normal for bazzite on Steam Deck)
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