Okay, so I checked possibly everything and here are the outcomes.
1 - It definitely happens quite noticeably in CollaNotes as the first video shows.
2 - It happens in Apple Notes as well, although less noticeably. When you write longer stuff it becomes more noticeable. Here is the video of it happening: https://youtu.be/7JrxpsIlaD8
3 - It does not seem to happen in GoodNotes, so I’m assuming it might be a software issue; although it is weird the exact same thing happens in Apple’s own app as well. Here is a video from GoodNotes: https://youtu.be/UhIVhKHLg0M
4 - I tried unpairing and pairing again the Apple Pencil. The problem occurs when I write with my finger and not with the Apple Pencil as well, so I think it is not related with Apple Pencil.
5 - I am using the display in "More Space" mode. When I tried to switch to the "Standard" mode, both black tint and jiggling issues have gone away.
Overall, the issue seems to be related with the software, specifically with the "More Space" display mode and Apple Pencil Kit or the handwriting frameworks in these apps not working well. GoodNotes seems to be doing fine in either case.