The odd thing is it is not usually the electrons that have the energy, they are just drifting around doing whatever feels right based on the local gradient of the electromagnetic field.... but then the field is defined by the distribution of charges and their motion....
And it gets weirder than that, as energy can move in just the electromagnetic field itself, without any electrons being there at all - like radio waves travelling in empty space, as does light.
At DC and low frequency AC it is much like a hydraulic system, where the fluid is incompressable and power appears at the other end of a wire At high frequencies it becomes more like sound, where you get echos and reflections, and you are interested in how waves move in the medium.
Electrons are like water or air molecules in those analogies - a drop of hydraulic oil or an atom of air has no sense of the bigger picture, it is just doing its own thing and moving with the flow.
I am sure that didnt help you one bit, but ponder on it - a regular motion of charge can induce a wave in the electromagnetic field, and likewise waves in the EM field can cause a charge to move - this allows you to move power around, manipulate it and transform it without moving the actual charge carriers very far.