There is a very interesting tech using superconducting loops to store power. I think that that will be the 'battery of the future' but it is going to take a while before that sort of thing is safe enough (and cheap enough) for things like vehicles. But for stationary short term 'ride through' situations it has already been deployed, and also for stabilization of the grid in the presence of fast fluctuating loads or generators.

Superconducting storage is inherently short term, as the capex per unit of energy storage capacity is rather high. I doubt it's competitive with batteries even for diurnal storage. It might have niche uses, for example smoothing demand (on time scale of hours, not days) from intermittent high power users like electric arc furnaces.