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The article says the spheres will be at 500-600m depth, so something like 50-60 atmospheres of pressure. Compressing air enough to displace water at that pressure would heat it to extreme temperatures which must be very inefficient even with some attempt to recover the heat. Water being incompressible can I assume be moved in and out of the sphere without any heating (and, therefore, energy loss).

(I'm guessing, of course)

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One probably wouldn’t want to store energy by adiabatic compression like that. Instead one might try to approximate isothermal compression, perhaps by using multiple stages with heat exchangers to adjust the temperature between stages. IIRC there was a startup, Lightsail Energy, that had an idea of using a water mist as either a heat reservoir or a phase change medium, and I don’t know whether they ever got it working well.

I hadn't thought about heat. While the air will be hot, that heat was already there (the heat energy in 50 liters of air compressed into 1 liter, just like the compressor in a heat pump). I think this makes it even more viable, as the air pump/compressor can use that heat to partially power itself. A water pump can't do that.

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