Electronic data is energy stored.
But under opposite goals - you're confusing information density with energy density.
Electronic data storage uses the least possible amount of energy to store the most possible amount of information in the smallest space.
Battery storage, while willing to go complex if necessary, is trying to store the most amount of energy in the smallest space.
So there are literally opposite energy storage engineering schemes at play.
Unless... you could create gate switches in the actual stored energy, or (more likely) in the electromagnetic energy fields generated by the stored energy itself. In which case the energy density of a battery would also be information density, which would be majorly slick.
But the opposite isn't true, because energy density approaches minimal in purely information storage, because of the heat and durability issues that affect semiconductors.