Based solely on this drawing – since I don’t have a datasheet for the PWM controller depicted – it looks like the potentiometer is there to provide a DC bias for the input Aux signal. I draw that conclusion based on the fact that the potentiometer has its extents connected to Vref and GND, meaning that turning the wiper would be selecting a voltage somewhere in-between those two voltage levels.

As for how this controls the duty cycle of the PWM, it would depend on the operating theory of the PWM controller. I can’t quite imagine how the controller might produce a PWM output, but I can imagine a PDM output, which tends to be sufficient for approximating coarse audio.

But the DC bias may also be necessary since the Aux signal might otherwise try to go below GND voltage. The DC bias would raise the Aux signal so that even its lowest valley would remain above GND.

So I think that’s two reasons for why the potentiometer cannot be removed: 1) the DC bias is needed for the frequency control, and 2) to prevent the Aux signal from sinking below GND.

If you did want to replace the potentiometer with something else, you could find a pair of fixed resistors that would still provide the DC bias. I don’t think you could directly connect the Aux directly into the controller.