Faucet dripping only when water main shut off
Single handle faucets or washer less actually use the pressure as part of the mechanism to stop the flow, when the pressure is reduced two far some start dripping. I usually have standard rubber washers and several sizes of O-rings for washerless faucets to replace when they start dripping, if after the pressure is restored the drip has stopped I would not worry until it starts dripping with normal pressure. Usually once a washerless starts dripping you have months to repair.