There's a neat video by smarter everyday (and a bunch of back and forths among youtubers, including electroboom) where they show it and argue about it, but the power is actually transmitted through the electrical fields 'outside' of the wires.

Imagine a loop of electrical wire that is 300,000km long. Your switch is at point A, and the light bulb is at point b, halfway along the wire. If the energy truly 'propagated down the line' it would take half of a second for the light bulb to turn on when you flipped your switch to complete the circuit. Interestingly, if you make the loop so that points A and b are closer than the lines maximum possibility (or, in other words if you imagine the loop as a 0, the points are at the left and right of the 0 instead of the top and bottom), then the light bulb turns on based on how far apart the points are, not the distance of electrical line between them.

Nah. Power is just the potential to do work. Clever electrical engineering just takes advantage of the teensy pushes and pulls to do that work. Like pushing a swing, I don't move but my kid sure can go high when I apply those pushes and pulls at the right time.