Serpentine belt squealing and jumping?

Jumping off a pulley, jumping off-center to one side, or just vibrating a lot? A lot of vibration suggests one pulley is tight and doesn't want to rotate. Squealing means the belt is sliding across one of the smooth pulleys as it goes around it. That is caused by that pulley, or the one right before it being tipped or turned. The spring-loaded tensioner pulley is a common cause and a good guess for that, but also look at any other idler pulleys and the water pump pulley.

What is the condition of the belt? Do you see fraying and white strings peeking out on one edge? Has there been any kind of belt dressing applied to it?

Smooth metal pulleys were painted black at the factory. That paint wears off as the belt runs over that section. With the engine running, look for a pulley where the belt is running to the side of that shiny area now. That also indicates that pulley or the one just before it tipped or turned, usually due to a worn bearing. The pivot arm of the tensioner pulley can develop wear too and allow that pulley to droop and tip. Since it has been replaced already, check that it is mounted squarely. There's a tab on the back of the mounting plate that must sit in a hole to keep it from working loose and rotating. I've had a couple where I didn't get that tab seated correctly the first time.

Check out this article too for more information:

https://www.2carpros.com/articles/car-squeaking-noise

Let me know what you find.

Thank you for the dandy video. It appears one of the items run by the belt has bad bearings on its shaft. You can see that by the way the belt is moving back and forth near the bottom of the picture. That is also causing the knocking noise.

I would remove the belt from one of the pulleys to release its tension, then rotate and wiggle each pulley to find the one with excessive movement. Let me know if that pans out.

I would be very surprised if just the hub of the pulley is worn. If it's that loose, you should be able to pull it off with one hand. More likely the bearings the shaft rides on are worn. That's actually usually a bronze bushing. I can add two comments of value related to power steering pumps. First, in over 30 years as a suspension, steering and alignment specialist, including ten at a very nice family-owner Chrysler dealership, I've only run into two power steering pump problems. On one at the dealership, it was perfectly quiet but gave no power assist. Once the belt was removed, the entire shaft with the pulley still on it pulled out, then fluid started to dribble out. The shaft wasn't turning the pump, but there was no vibration or noise.

The second problem has to do with someone right here I'm working with right now on a PT Cruiser. His new pump came with the pulley already on it, but it's set back too far. We haven't figured that one out yet. Most of the time when you order a new pump, it comes without the pulley. You need a special tool to transfer it to the new pump. The job isn't terribly difficult. If it comes to that, you can borrow the tool from an auto parts store. I'll post hints to go along with the instructions that come in the tool kit.