Lovelace Climate Card Battery Level

I am not aware of a means to put it into the thermostat card without making a custom card.

If you just want to pull that data into a sensor, see the example below.

https://github.com/SilvrrGIT/HomeAssistant/blob/master/sensors/zwave_batteries.yaml#L14

If you have a lot of battery powered sensors, you may want to look into something like this