TL;DR: I had an issue where after disconnecting the Legion Go from my TV, the main screen would show static with no way to recover but to power cycle. To solve the problem I force the Display to 1920x1080@60 (go to Settings > Display > Resolution when connected to the TV)
I did not find reports of this issue anywhere else, but when searching for static or fuzzy display on google I landed on this this thread and this this trick (now removed) . While those two links were trying to solve a different problem, they both mention that the Legion Go screen goes static becuase it can only handle either 60 or 144 Hz. This notion made me think that steam OS gets confused when switching from the TV to the internal display and forgets to set the correct refresh rate. I am not sure this is the reason, but the fix I apply to force the external display to 60 Hz seams inline with the reasoning.
I am running Bazzite 40.20240528.0 and the TV in question is an LG C1.
Posting here because as I said I didn’t find any other documentation about this issue as well as to give visibility to the developer community so maybe it can get patched.