I'm sorry that you are having so much trouble with your laptop.
I was likely the person who recommended that you do a factory reset -- and my motivation for that is the fact that with a PC with switchable graphics, such as yours, the only video drivers that are reliable are those from HP. Thus, doing a factory reset would automatically install and load those drivers.
As to the Windows version, HP does not tell us what version of Windows runs on each laptop, nor do they tell us what version was originally installed. In your case, it looks like that version was 19.09. And, since you are not seeing an update for 20.04, the that update is likely being BLOCKED by Microsoft, and that is probably due to the graphics situation.
We can do nothing about that because we can't force MS to release the block on your model PC, and we can't pressure HP into writing drivers for newer Windows versions.
You said you tried newer Windows versions on your own and those did not fix the issue. But -- did you back off the HP drivers before those installs and restore them afterward? Since you did not mention this, I am guessing you did not. If your forced the newer Windows versions through your own installs, you did NOT get HP video drivers -- and that could be a major basis for seeing no improvements.
So, I suggest the following:
1) Follow these directions for backing off the HP drivers on your PC: https://www.tenforums.com/tutorials/68426-backup-restore-device-drivers-windows-10-a.html
2) Install a newer version of Windows from the media you used before
3) Restore the HP drivers from the backup you made.
See if that makes any difference.