The problem with your description is that park and neutral should
behave exactly the same as far as the engine is concerned. The only
difference between the two is that park engages a parking pawl to
keep the car from moving. Other than that, (and the position of the
transmission lever) the two positions are both neutral.

Since the noise goes away when you remove the belt tension, one
would suspect that the noise is coming from either the alternator,
a/c compressor, power steering pump, or one of the idler pulleys.
Or, one of these pulleys is brushing up against something when the
engine is rotated slightly when not in gear.

You can either live with the noise, or take off the belt and spin each
accessory by hand to see which one clicks. Or use a length of heater
hose as a stethoscope to try to pinpoint the problem.

Bob