Can someone maybe tell me, how are the chances that it is on my laptop (graphics card or something) or on the new display?
Very likely on the display.
(I understand correctly: the error came with the display change?)
Incidentally, pixel errors are not that rare; I also have such a permanent point (visible only when black picture is shown).
The display in front of it was completely destroyed, so no idea.
This is definitely a pixel error in the panel… A little insider tip from me… Sometimes such pixels can be revived by light pressure / massage
Which also often occurs are cable / connection error between device and display (in the hinge). They often show up when the easy display is opened / closed. But show a different defect image (not individual pixels, but streaks, stripes, patterns).
A (theoretical) possibility would be a cell in the video memory. As a memory test (Heise / CT download) can help (maybe your bios has something in it).
But I do not really believe it: for me it looks like a typical display pixel error.
No doubt, it's up to display. Even if it disappears, it will come back.
Whether it is a complaint reason depends a little on traders (see ISO 13406-2).
I would report to the dealer that the display is faulty and would require an exchange.