What is the major source of engine noise for non-propeller aircraft?
At full power it is the mixing process of the fast exhaust flow with the surrounding air. Note that noise increases with the sixth to eighth power of jet velocity, so the loudest engines are those with a low bypass ratio  and reheat on.


Diagram from a Stanford web page on noise. The jet velocity is in ft/s.

At idle the biggest noise source of the whole aircraft is the flow around the lowered landing gear, gear cavities and the slotted flaps that you asked us to disregard. The engine noise is a combination of intake noise, bearing noise and nozzle noise, and which of those contributes most to the engine noise depends on the individual engine and its installation into the aircraft.