2004 Chevrolet Silverado continuous chirping noise

Sprinkle a little water on the smooth backside of the belt while the engine is running. If the noise changes, it's belt-related. Look for any pulley that's turned or tipped. If you sight down the pulleys, you should not see the belt peeking out to one side even 1/16" on any one of them. If it is, that means the belt has to walk sideways across a pulley as it goes around it. Normally that causes a squeal.

Chirping can be caused by tiny rocks and other debris embedded in the smooth backside of the belt. You have to be very careful, but if you hold the sharp end of a flat file lightly against the belt where it goes around a grooved pulley, you'll see little sparks each time a rock chip hits it. If you hold more pressure on the file, eventually those chips will fall out.

The only thing I can add is if any type of belt dressing was used previously, scrub all the pulleys with soap and water, then install a new belt. No belt dressing products must ever be used with serpentine belts because small rocks and debris will stick to the belt and become embedded in it. That will set up more squealing.