An AC compressor can make noise for a few reasons.
The clutch/pulley bearing is worn. This noise usually occurs if the AC is being used or not.
The AC compressor clutch is worn. This noise usually occurs when the AC is engaged. But I’ve seen compressor clutches so warped that the disc rubs against the pulley even when the AC isn’t engaged.
The compressor itself may be self-destructing internally. When this happens, the entire AC system must be totally rebuilt.
Take the vehicle to an independent shop, and get a second opinion.
Take the car to a good independent shop near you, use Yelp if it’s the only thing available to find one. Another option is to look up an ASE Blue Seal Shop near you:
Either way, find a shop near you and get a second opinion. If the problem occurs even with the A/C turned off (make sure you don’t have defog on or the car in recirc mode) you might get by with just an A/C clutch replacement if the noise for sure is coming from the A/C compressor and not the alternator (which was shown in your vid). Either way, a good shop should be able to tell you.