So let's stop talking about energy and start talking about power.
The battery is a source of power. The LED/resistor is a consumer of power. The LED lights up, so power was transferred from the battery to the LED. The capacitor is between the battery and the LED. What kind of power went through the capacitor on its journey from the battery to the LED?
Why it is hard to understand the concept of energy storage.
There is nothing going "through" capacitor but in to capacitor.
You need wires to transfer energy from the source to the capacitor and if you also add an LED to the wires it makes no much difference other than reduce the speed at with the energy is transferred to the capacitor.
Is sort of like you want to believe that electrical energy can pass through in order to deny that energy storage exist.
There was a good reason I replaced the energy source with a charged capacitor as I was thinking one way or the other you can understand that capacitor is an energy storage device.
Electrical power is product of electrical current and electrical potential. I think is clear that you can not have electric current flow through air at least not with 20V and 1m of distance so there can not be any power.
You only have an electric field inside the capacitor once you have an imbalance of charge and not the other way around.
All this are well known facts but thanks in part to Derek facts are no longer relevant if you can make absurd claims like "energy doesn't flow in wires" and back them with no evidence. Show a waveform that you do not understand and say here is the proof.
His channel will more appropriately be named mendacium even if he's intent is veritas.