Clearly the oil is leaking from the bottom of your air pump.
You know that cylinder with black metal bracket on the right side of the cylinder head just above your coolant thermostat.
Its what provides your brake master cylinder with air pressure, and works off the exhaust cam.
One of your pictures is of the underside of the Air Pump, showing both it and the black bracket covered in black oil.
There is a metal oil gasket in there.
Remove the black metal bracket, remove the three torx bolts, and pull the air pump and examine or replace the gasket.