Seems like at least one company solved this problem. I have Asus TUF monitor (I don't remember exact model, but they should be similar) and LED indicator is almost unnoticable at night, but enough to see if the monitor is on.

[0] https://www.pcomp3000.pl/images/produkty/Monitory_32/VG32VQ/... (I couldn't find higher resolution image, the indicator is on the bottom right)