Fan in tiny bathroom has no vent. Is there a better option to absorb/reduce moisture/odors?

I lease an apartment and was just cleaning the light/fan combo (a NuTone NUA-40LN) in the ceiling of my very tiny but full bathroom and realized the fan in the ceiling is just blowing air around, but not actually out anywhere.

It’s an old unit, and I imagine there might be better options now for folks who can’t vent outward.

I live in an old building and my landlord isn’t likely to pay for any sort of line. But I could make the case for replacing this unit and would be cool with doing it myself if you know of better options. Thanks in advance!