https://www.researchgate.net/profile/Marie_Maar/publication/...
I'm not very bullish on the technology however, maintaining anything in the ocean is a difficult challenge. My guess is a mixture of batteries and power to gas would probably wind up being easier to scale up, and cheaper in the long run.
When you go under water the pressure increases and you have to pump against this pressure. The formula is (if I recall correctly) (P0 + rho * g * D) * V with D the depth under water and P0 atmospheric pressure. Ignoring P0, you would need a reservoir 700 meters above ground to store the same amount of energy in the same amount of water. A 700 meter water tower is harder to build than an underground reservoir.
They're in the Alps. Why not just put a bag of water uphill. Fill it using excess energy. Drain it to run a turbine.
Opportunistic use of caves and the like could hardly ever be worthwhile because it does not scale.