That's not how electric current works. It's more like a wave in an ocean. A wave may travel from Hawaii to California but no actual water molecule moves that far (or even very much at all). Electric current is a wave of excitation of electrons, which is what moves at the speed of light. The actual drift of individual electrons in the current is much, much slower (and IIRC in a superconductor is zero).

Nowhere, it's still there - a loop of superconducting wire would also be a perfect energy storage because the electrons would just keep going around without any loss(it would be an extremely small capacity storage though, superconductors lose their superconductivity at high enough amperage which is basically what introducting more energy into the system would be).

Why would the electrons spread evenly?

They move over to the other side and back and forth resulting in an oscillator.

That causes all your energy being radiated into the surrounding via radio waves.

That is how your microwave oven works but instead of a superconductor it uses a magnetron with free flowing electrons.

Current in a conductor does not involve the potential energy of charges (electrons) being concentrated. This should be clear by the fact that currents cause magnetic fields, but do not give the conductive wire a charge gradient (or an electric dipole moment).

Superconducting circuits can still have AC loss. You’re basically describing discharging a capacitor through a superconductor. If there’s no loss anywhere, it will be be an LC oscillator. If there is loss, the energy will dissipate.