Fan solution for interior bathroom?

I want to add a fan to my bathroom mostly just for noise purposes. The bathroom has no walls to the exterior of the building. I am in a condo so going through ceilings is not an option, and would prefer to not have to dig into the walls the way most ductless fans that are flush-ish against the walls seem to work. There is a vent but I think it just goes into the space between the walls as opposed to outside, so I probably shouldn't draw a ton of moist air in there and make mold, and even if I could the opening is pretty small (less than 6" x 6" and 3.5" deep for the part directly behind the vent).

https://imgur.com/a/qCfCQUw

Is there just a thin and fairly discreet looking fan box I could mount directly against the wall on the other side of the bathroom? Open to any other ideas too obviously - as you can probably tell from my post I am pretty unhandy/uneducated about this kind of stuff. The main goal is giving people a way to at least somewhat cover up noise when using the bathroom, with any odor reduction a secondary benefit.