Well dang. Reading this article does provide q couple more details though:
* Another referenced study DID find that closing the lid reduced contamination
* It depends on the toilet shape
* Closing the lid does change the areas that get contaminated in the room:
https://www.ajicjournal.org/cms/10.1016/j.ajic.2023.11.020/asset/171d40ff-18ca-4d0c-9897-5d94d0282ebd/main.assets/gr3.jpg

All in all (including my first point that most trips require it down anyway) and as a matter of personal preference (I think its nicer to have the lid closed), I’ll continue to close my lid.