When lowering the hardware brightness (either through the monitor OSD or through DDC), the voltage of the LED backlight gets lowered and thus the LEDs get dimme

When lowering the hardware brightness (either through the monitor OSD or through DDC), the voltage of the LED backlight gets lowered and thus the LEDs get dimmer and less light passes through the crystals. Polarization doesn't come into effect here. What you're describing happens when lowering the brightness through software (either Gamma adjustments or a dark overlay) because in that case you're only changing the software pixels to be darker. Although even in that case, newer miniLED/quantumDot LCD screens also lower the LED brightness when pixels get darker, because they have more granular control and dimming an LED doesn't cause shadows over a large area of the screen anymore.