Seems to be a standard K&N crankcase breather filter common on car setups. It will give off light mist of oil vapour (my large oem style k&n in hamcan airbox does this at idle, hard to see unless sunlit just right and no wind, looks like light smoke).
Any vapour will leave oil build up as it cools on surfaces. I'd expect a puddle of oil in the hose if it is the lowest point before filter. That's why a catch can is used in many bikes/cars.
My modern Triumph has a short bit of tubing off bottom of airbox to accumulate this condensed oil vapour. Tube is sealed off at bottom end. Supposed to remove, drain and replace at regular intervals. Hardly anyone ever does it. No harm comes.