Butters outstanding logic, no wonder you are struggling with this concept
If you have run out of power, you are at max power so it most certainly is 'with power'.
Yes, the engine is running, and thus producing power, but by that logic you could call a normal landing, "settling with power"!
You've been banging your head against that wall too much!
The term "with power" means "with power available", not simply, with the engine running!
Being at max power by itself will not cause you to settle. However, if max power is not enough, then you will begin to settle due to a lack of additional "power available"! It is not called "settling with power" because you have no more power available!
If you did have more power available the only way you would start to settle is because you have entered the vortex ring state, which is why we call it settling "with power". You have power available, but are still settling!
Just when I think I'm out, they drag me back in!