There's a very, very simple solution to the bug shown in the first part of this: have the in-game inner dead zone set to anything above 0. I had set mine to 0 at the very beginning of my playthrough due to usually preferring to have Steam Input handle deadzones, and other games I play work just fine with similar settings. Cyberpunk, however, recognizes joystick input when there is none, causing problems unless the deadzone is set to anything above 0, even 0.01.

I also do some some light comparison between FSR 2.1, FSR 3, and XeSS to try addressing the blurriness in the previous video. tl;dw: I think it was mostly caused by FSR 3, and have switched over to using XeSS.