there is always some DAC (digital to analog converter) unless you listening old tapes or vinyls on analog devices
if you compare absolutely same headphones it will cost you more power over BT because you have to encode audio for BT protocol, transmit, decode BT protocol in headphones …
if you use wireless charging you loosing about 10-20% of power, poor alignment may loss up to 70%, small devices has efficiency about 50% because of small coil. so wireless charging should be restricted especially in EU what trying to be green world saver with their unified connectors and so…