Washington is one of the dozen-plus states with the strongest rules against messing with electronics while driving. RCW 46.61.672 says simple "A person who uses a personal electronic device while driving a motor vehicle on a public highway is guilty". "Using" is defined as "Holding a personal electronic device in either hand or both hands", which means what it says (literally, holding: the thing can be turned off). It also means
Using your hand or finger to compose, send, read, view, access,
browse, transmit, save, or retrieve email, text messages, instant
messages, photographs, or other electronic data; however, this does
not preclude the minimal use of a finger to activate, deactivate, or
initiate a function of the device
A personal electronic device is
any portable electronic device that is capable of wireless
communication or electronic data retrieval and is not manufactured
primarily for hands-free use in a motor vehicle. "Personal electronic
device" includes, but is not limited to, a cell phone, tablet, laptop,
two-way messaging device, or electronic game. "Personal electronic
device" does not include two-way radio, citizens band radio, or
amateur radio equipment.
It does not matter whether the device is a watch, phone, brooch or whatever.
Oregon's law ORS 811.507 defines the crime as:
A person commits the offense of driving a motor vehicle while using a
mobile electronic device if the person, while driving a motor vehicle
on a highway or premises open to the public:
(a) Holds a mobile electronic device in the person’s hand; or
(b) Uses a mobile electronic device for any purpose.
Condition (a) covers what Washington law says, but Oregon adds "or uses it" (which covers the case that you use it without holding it). "Mobile electronic device" is defined as "an electronic device that is not permanently installed in a motor vehicle" – e.g. a watch.
It appears that you'd have to do a state-by-state check to see what's legal. Under the letter of the law, listening to music on your phone (or similar device) is legal in Washington as long as you don't hold it at any time while driving, but not in Oregon unless the device is permanently attached.