I belive that you will find when you take it out that it’s the fan blower moter. It is started when the key is turned on and before the truck is cranked. Then it takes a bit to spin down after the truck is turned off. The fan bearings may be worn out or the fan cage itself may have something in it, be out of balance , loose or broken.
100%! When you add the guy’s description of the thing looking “cylindrical” and “hat shaped,” and there’s little else it could be!