Yeah the gas laws like to say things like “an ideal gas in a closed system.” Storing energy by compressing gas, using the gas basically as a spring, is trying to take advantage of Boyle’s law, while trying not to run afoul of Charles’ law. Take a parcel of room temperature air and compress it. The total amount of heat energy remains the same, but the temperature skyrockets. Because of a temperature gradient, some of the heat energy will pass into the compressor machinery, the walls of the air tank, any pipes and hoses etc. and radiate into the environment, so that when the gas is allowed to expand to ambient pressure again it absorbs heat to do so, imparting less energy to any pneumatic motor it is expanded in than went into compressing it.

An insulated tank might help mitigate that but for the sake of the bearings and packings I’d suggest against insulating the compressor cylinder.