I remember watching a video where they added some liquid visible with UV to the water and flushed, there were droplets everywhere including the tester’s face.
It’s not a study but it’s enough to make me close the lid, especially when my toothbrush is in the same room.
Yes, toothbrushes live uncomfortably close to the loo in my house too.
A friend gave me some light banter about closing the lid = under my wife's thumb but it's absolutely about me attempting to keep the toilet business contained to the toilet!
Someone once tried to argue against it by saying it still got the droplets in the air with the lid closed so there’s no point. My counterargument was that it still contained a lot of the droplets by closing it and that it’s the most minor of inconveniences to close it so you should just do it anyways.