Energy transfer doesn't seem like the whole explanation. As a thought experiment, mount an (unfeathered) propeller on a shaft running in ball bearings on an airplane wing. Mount an identical setup on the other wing, but lock the shaft so it can't rotate. The energy transfer will be (essentially) zero on both sides. Will the drag be the same?
Here's how I'm thinking about it: The angle of attack of the propeller blades depends on the airspeed (of the aircraft) and the propeller's RPM. Under power, the propeller advances forward on each rotation by an amount less than its pitch. This means that the blades operate at a positive angle of attack and make positive lift -- aka forward thrust. If the propeller advances by an amount equal to its pitch on each rotation (perhaps during a dive), the blades operate at zero AOA and make zero lift and zero thrust (or a little, depending on the airfoil).
A windmilling prop advances more than its pitch on each rotation. This means it operates at a negative AOA and makes negative lift (i.e. drag as seen from the perspective of the aircraft). Lock the propeller from rotating, and the AOA goes so massively negative that the blades stall. They then stop making negative lift (but there's still significant drag, of course). Or better, feather the prop and reduce (or is it increase?) the AOA to near zero.
If a windmilling propeller was mounted in bearings and was 100% efficient aerodynamically, it would rotate fast enough to advance an amount equal to its pitch, bringing the AOA to zero. But there's always drag, so it can't spin that fast. Add a rotational load to the aerodynamic drag, and the propeller spins even slower, increasing the negative AOA and negative lift/drag. At least to up to the point where the blades stall. So the energy transfer does matter.
This all seems relevant to the fan in a jet engine. But I know there's a lot of other stuff going on that I don't understand.