Horizontal lines appear when using Apple Pencil on iPad while charging
I seem to have found a solution to my own problem, so posting it here in case others have the same issue.
I have been charging my iPad from my Macbook, which was also charging at the same time. As soon as I remove my Macbook from its power source, the issue disappears. It seems that the AC power entering the Macbook was somehow interfering with the iPad!