The case communicates with devices. That uses battery. I think the case and pods are pretty active so that they can connect quickly.
The case itself only seems to connect to the AirPods - and any communicate to a Bluetooth connected devices is via the AirPods. If you remove both, you won't get any communication from the case itself.
Also, when the case is closed, the AirPods don't show up as a device that you can connect to from iPhone, Watch or Mac. However the AirPods do seem to be doing something while in the case - as if they were fully powered down or sleeping, the battery wouldn't be depleting at this rate.