Could be either/or. I long ago lost the brassiere that came with my AirPods Max (not really lost, I just can’t be arsed to dig it out of where I think it is) and they’ll drain themselves fairly quickly just trying to throw out stray connections to any of the five or so devices they can connect to unless I make a point of disconnecting them. AirPods Pro exhibit the same exact symptoms when the contact inside the case needs to be cleaned.