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Baseboard heating normally uses hot water which heats the air through the fins. It doesn't generate dust bunnies..... then there is also electric which works on the same basic principal. There are no fans or blowers.
I would vacuum inside the radiators. They do come apart fairly easily. Get behind them - the areas between the back of the radiator and the wall. Vacuum well and put back together.
I think I'd be a little bit more concerned about the water damage I see around the air conditioner and the possibility of mold.
You know... it really looks like dust birds. Do you have ceiling fans?????
The dust bunnies look suspiciously like blown-in cellulose insulation. Is that a true vent with airflow you can feel if you hold your hand near it, or just and electric or hydronic heater? If there is forced air heating, my bet is that rodents have pierced the ductwork and are making nests in it with insulation. It is a landlord issue either way. That is not normal.
^^^^The bolded part. My first impression is that it looks like insulation.