The exact model of the pen, as listed in the original post, is "TOUCHPEN WCM 11051B6 D6.5 SG A Pen", this is what is given to me in the spare parts manual of my Laptop. The product number of my laptop is 82DE0009US. It's a yoga 9i, 15". I'll try to attach a picture where the problem is clearly visible. I think I know how I could do that. I have attached two images:
one of them shows me holding up the pen to a photoshop window, and the other shows simply the mouse pointed over the window There is also a window of the Lenovo Pen settings app to show that it is the bottom button that is, indeed, the one that is stuck. As you can see in the picture, when I'm holding the pen up to the screen, the tool shown in the canvas is different to the tool shown when I simply hold up the mouse pointer. The tool shown is the eraser tool, and it is being selected by the lower barrel button, which, as you can see in the picture, is not being pressed. I was going to use One Note to prove this was the case (because I get the same problem across all apps, which is how I concluded this was a hardware problem), but One Note no longer shows an Eraser icon when erasing.
Since my device is out of warranty (as implied by the original post), I am not expecting to get a replacement for free, but I just wanted to know how I could get a replacement myself or fix the issue by opening the pen up and fixing the stuck button.