One probably wouldn’t want to store energy by adiabatic compression like that. Instead one might try to approximate isothermal compression, perhaps by using mul

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.