It doesnt need refrigeration for storage, CO2 is stored at higher pressure

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

Yes, the critical point for condensation of CO2 is 31 C:

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.

Charging batteries also produces a huge amount of heat. In general, storing energy is never free. It's the tyranny of the second law of thermodynamics.

Though they could store some of this heat for later when they want to extract the CO2 gas again, I suppose.

Which according to the article is what’s happening. They store heat in steal piles, and release it back on expansion.