It very well could be the belt tensioner. They fail from heat over the years.
It's about a $150 dollar item. You would / should also replace the little belt shock absorber, and the adjuster rod. The serpentine belt is not $15. More like $40 to $50 dollars.

My experience is that when your tensioner is bad, it only reveals it's condition after you have replaced some rotating accessory on the front of the engine and are attempting to re-tension the belt. It won't tighten up and then you get to order the parts and wait. Happened to me 3 times now.

You know it also could a failing air pump. That also happened to me. The screech was really loud.
It went away after the pump shut off. Then I unplugged it. You need to have someone start the car while you stand in front with the hood open. You should be able to be an idea of where the noise is coming from. Air pump is on top left as you are looking at the engine from the front.

Steve