I would like more detail on the "Thermal management system" and how long it could store the heat it captures. One of the benefits they touting is "Long duration energy storage" I would think the limiting factor would be the ability of the thermal management system to retain the energy it captured to reheat the compressed air. Am I thinking about this correctly?
A possible component that might be missing (in the thinking and/or in the proposed implementation): the stored heat could also be utilised separately if needed, so if you have an intermittent heat consumer and an intermittent electricity consumer you could consume the heat first, then leave the remaining compression energy (what you could recover without reheating) "forever". Bonus points if you also happen to have a coolant consumer to benefit from the temperature delta caused heat loss or premature heat consumption.