I know you didn’t ask me but since I had similar issues and followed @paulakreuzer’s attempts also, I thought I’d chime in.
As far as I know, the new screen didn’t help. (See comment here)
I don’t know if your problem is the same as mine was, but my issue was fixed by sending the phone to be repaired. I’m not super knowledgeable in these things, but I tried explaining my issue and everything I tried as best as I can in this thread. I’m not exactly sure what the issue in the end was, but FP support thought that it might be a problem with the GPU, and the issue was fixed by changing the motherboard/core module. If you’re better than me with tech stuff (which, admittedly, is not a very high bar), you might be able to fix the issue without having to change the whole module, but for me that was the only thing that helped.
It’s been maybe a year since my phone was repaired, and the problem hasn’t come back so far. I mean, my phone is slow at times and I do get the occasional noisy/pixelated stuff, but I barely even notice it (it’s nowhere as bad as before, just a few pixels here and there once a month or so).
Hope this helps!