Yes this is a common issue on FP4 sadly. Lots of huge forum threads about it and basically no response from the company after years of asking. Installing a new screen seems to sometimes fix it but not always. (Someone suggested a sort of "pair" behaviour, where some screens work fine with one device but not the other) I had it on my phone too, but it kind of just went away almost completely. Anecdotally i feel like there might be a correlation between low battery and frequency of ghost inputs. Have you tried resocketting the display cable yet? That seems to have helped many people and is fairly easy to do and free.
I finally tried resocketting the cable, and I've only seen the issue a little bit since, but not as extreme. But I'm not sure if it's real or just my perception ;). I'll keep an eye on it. Thanks for the idea!