Can you point to a source of these superconducting energy storage mechanisms? How do they work? I briefly looked into it and found out that at least the current ones have very high power density, but low energy density.
""" Although the attainable magnetic flux density limits the energy per unit volume given by Equation (1) ( B2 /2μ o), the real limit of the energy stored in a SMES is mechanical. [...] The relation defines the minimum mass of the mechanical structure in pure tension to support the radial electromagnetic forces. Force-balanced coils [5] minimize the working stress and thus the mass of the structure. """
So it looks like they 1) don't look at cryo and 2) the limiting factor is the stress due to EM fields.
[0] https://snf.ieeecsc.org/sites/ieeecsc.org/files/CR5_Final3_0...