It looks like I have found the cause of the problem. I have a long cable to the display (about 1.5 meters) because the printer is large, the electronics are in the back, and the screen is on top in the front.
If there is too much cable running along the profile of the printer, then there is a problem with the registers.
If I remove the cable from the printer profile (like on the picture), the problem disappears.
Currently, this printer’s outlet does not have a ground connection.
The power of the printer’s LED backlight does not seem to affect the problem.