GAW, i don’t think you can compare a wrist watch battery which is a perpetual battery to a toy battery or a phone battery which needs to be recharged or turns the item on and off. It is not the same thing.
In addition the battery also controls the light of the phone. The light of the phone is off or dim, only when you press the key does it turn on. The watch always works and it has nothing to do with whether you touch it or not.