Your pretty gross example covers all the toilets on several university campuses I've been to as well. Very common

They s shaped pipe hasn't been invented there yet (things may have changed in the past ten years though, but certainly not all bathrooms have been remodeled that quickly) and so the sewage pipes regularly blast out burps of stinky poo smells into the restrooms. This happens in student dorm rooms too if you have the top tier ones that have a private toilet for the room as opposed to a huge communal one.

It depends on region (and date of visit), I guess. I was in Beijing 2 years ago (so slightly pre Covid) on a business trip and while there are negatives, the toilets there were great.

I guess that’s because Beijing is a rich region, I really don’t know, were not anywhere else

Beijing gets a lot of care because that's where the rulers live and where a lot of tourists go. It got cleaned up a lot before the 2008 olympics because it was showcasing China.