Pencil 2 won't pair with 2024 iPad Pro

I upgraded from the 2022 iPad Pro to the 2024 version. I had an 2nd-gen Apple Pencil on the previous iPad Pro that worked well. But I didn't use it that much and had set it aside for several months. I wanted to see how it did on the new one, so I placed it on the magnetic strip and ... nothing. No pairing notification, no indication that it was charging.

At first I worried that it had undergone "deep discharge," which can happen to the Pencil (and other lithium-ion battery products) if they sit uncharged for too long. Basically, they die. I tried some tricks I'd found online, including gently warming it by wrapping it in a heating pad set on low heat. Nothing worked.

I'd given my old iPad Pro to my wife, so I thought I'd see what happened if I put it on there. Lo and behold, it paired right up, and charged right up! So I tried unpairing it, and then putting it on my new iPad Pro once I knew it was fully charged.

Still no recognition. It just won't work on the newer iPad. So, my questions:

Is it possible my iPad Pro has a problem with the charging/BT pairing feature? Should I bring this to an Apple Store, even though the pencil is old?

Is it possible the 2nd-gen Pencil doesn't work with the newest iPad Pro? Hard to believe, but .... I do notice that the magnetic strip on the 2024 model doesn't hold the Pencil as firmly as on the 2022 model.

Is it possible there's a problem with the Pencil? Though it works perfectly on the older iPad Pro.