How to air-seal apartment breaker box and range hood duct
Every residence, excluding the ISS, submarines and similar special cases, needs a certain amount of makeup air. Newer buildings tend to let in far less air as a way to improve energy efficiency, but there is always some air coming in or else you would end up with too much CO2 and not enough O. See Apollo 13 or a report of a mine disaster for details.
That being said, if the problem is excess draft caused by the bathroom fan, stop the bathroom fan! Since this is a rental, you can't replace the motion sensor without permission. But a piece of duct tape over the sensor will fix that problem really quickly. Alternatively, you could tape some sort of flap over the sensor so that you could turn it on/off as needed in order to ventilate moisture from the bathroom after a shower or bath. Much like many people place a removable cover over their laptop camera and remove it when they actually want to Zoom.