I write at the risk of having to admit that I missed the point in what you wrote. Apologies if I did.
Could you please narrow down the problem to a sentence or two at the most? The paragraph under " Desktop environment (KDE 6.3.4, LXQT 6.9):" says a lot but it seems to amount to “It’s broke”. We can’t fix it’s broke we need something more specific. The paragraph under " Description of the issue (screenshots if relevant):" does not seem to describe any issue. So if you could better help me understand that would be appreciated.
We will definitely need to know what intel graphics? The version matters. What is the output of inxi -G?
See if one of these existing topics fits your issue:
Display Driver Issue on Both ROME and ROCK (Intel-only System)
If none of those are relevant we need logs. Specifically we need logs from when you are having the problem. If you don’t know how to do this we can work it out once we get to a specific problem.