It’s called toilet plume.
A toilet plume is the invisible to the naked eye, cloud-like dispersal of raw, infectious sewage particles as a result of flushing a toilet. Flush particles rapidly rise out of the bowl and several feet into the air after flushing. Aerosolized droplets can remain suspended in the air for tens of minutes between users, posing an inhalation risk. These invisible particles go on to coat and spread onto surfaces like floors and counters or objects like hand towels, bathmats, or even toothbrushes.



YSK that your toilet lid isn’t a gasketed seal.
https://www.ajicjournal.org/article/S0196-6553(25)00630-3/abstract
Putting the lid down does reduce the amount of shit mist, but it does not even get close to eliminating it.
I’d much rather have something fall onto the toilet lid than into the toilet. That alone makes closing it worthwhile.
Got me there, but not really relevant to the subject here. Maybe make your own YSK post?
Kinda is tho: We’re discussing closing the toilet lid, so… yeah.