In short: as far as I can tell this invention is a new catalyst for increasing the efficiency of electrolysis.
But the catalyst is not better than current ones, it's just less toxic (and therefor cheaper). Which, while helpful, is far from groundbreaking.
The electricity can come from anywhere. Saying solar is just a buzzword to get people to click.
If not more efficient, is it at least a cheaper form of energy storage? (Platinum in the catalyst suggests no, although a very thin layer might be good enough.)
I'm not sure what you mean by whether it's more efficient than charging and discharging a battery. But the lifespan of a fuel cell is potentially indefinite and it does not require recharge(add in Oxygen and H+ any time and electricity starts to flow). Further, with each battery cycle, the efficiency of a dry cell decreases.
I think this electrolysis process can definitely make a cheaper form of energy storage than, say, batteries. Even though each anode requires small amount of Platinum, but considering the long lifespan of fuel cell storage, this form of energy storage costs much less than traditional batteries in the long run (all the toxic disposal!) And even for the purposes of propulsion, fuel cell discharge is much more efficient than internal combustion engines.