So depending where you are you'd need refrigeration
The refrigeration is needed because the process of compression produced huge amount of heat. And because of that, this method of storing energy is twice less efficient than batteries are
https://courses.lumenlearning.com/physics/chapter/13-5-phase...
However, I imagine you could wait for your too-hot-to-condense gas to cool and condense. That would probably be vastly more efficient than adding refrigeration.
It would depend on the materials used for the pressure tank, whether you can add more surface area and the external temperature.
You could even put the CO2 Tank under water in a deep lake/ocean. Then you don't have to have such thick materials to contain the pressure. The CO2 could be dissipating its heat and pressurizing as you pump it down (use a flexible tube so the water is compressing the CO2). For the return journey, use a rigid pipe so it doesn't lose energy pushing outward on a flexible pipe.
EDIT: https://en.wikipedia.org/wiki/Supercritical_carbon_dioxide, you can't slosh it.
Do you actually need to refrigerate it to keep it liquid? My SodaStream machine works with room temperature.