If these Shahed drones have a propeller they should have a brutal signature between 0-250Hz as they are moving a lot of air. And if the engine speed of the Shahed stays constant it will be even easier to detect it ("Angry lawnmower sound".. but that's only the high frequency part of it). There are extremely sensitive differential pressure sensors (like SDP600-25Pa) available from Sensirion that aren't overly expensiv…
What’s the frequency response of that sensor? The datasheet says nothing.
My experiments never had a dependency on linearity.