What the separator is actually doing
In a rotary screw compressor, oil is injected into the air end to seal the clearances, carry away heat and lubricate. The air leaving the air end is therefore full of oil, and the separator element has to coalesce that oil mist back into droplets and return them to the sump through the scavenge line.
Two things follow. The separator is carrying the machine's entire oil circulation, so anything wrong with the oil ends up in the element. And it is the only filter on the machine whose condition you can read directly from a gauge, through the pressure difference across it.