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.



I think it can help to lay some toilet paper down before you flush. I found it to be less smelly after doing so.
Before and after. Unless you like that little splash of dirty water on your taint.
Poseidon’s kiss. There’s no dread quite like using a porta-potty in a condition where there’s a risk of that happening.