Apple Pencil problem with screen protector on iPad Air 4 10.9"

I recently bought the new iPad Air 4 with the Apple Pencil 2. So far, it's worked flawlessly, but I wanted to use a matte plastic screen protector to have a "paper-like" feel. Upon installation, the finger sensitivity and touch was unchanged, but I noticed that the Apple Pencil did not register on the screen. The double-tap gesture worked, and so did charging and pairing.

To confirm that the pencil was not faulty, I peeled away a portion of the screen protector and used the pencil on the area, and it worked again. Then, I immediately switched the pencil to a covered area of the screen, and it worked for mere seconds before cutting off completely and not registering it. This process is repeatable.

The screen protector in question is made by UniPhone, and it is supposedly made of a PET plastic (polyethylene). https://www.ebay.com.au/itm/Paper-Like-Screen-Protector-PET-iPad-Air-4-Pro-2020-2018-10-9-12-9-11-10-5-10-2/264788064985?ssPageName=STRK%3AMEBIDX%3AIT&var=564757548923&_trksid=p2057872.m2749.l2649

It is NOT the official "PaperLike" screen protector.

I also tinkered with all the settings related to the touch accessibility, to no avail. Re-pairing the pencil did nothing. Both the iPad and Pencil were charged to completion, no change.

Does anybody have any experience with this type of screen protector? I have seen multiple videos online of this type of screen protector working flawlessly. Could this specific brand or material be interfering with the register? Or does the Apple wireless chip refuse to work through this material?

Any suggestions are welcome.