Send and Receive Messages
If you have a cellular-capable Apple Watch, you can send and receive both text messages and iMessages even when your iPhone isn’t nearby, although there’s a catch.
While iMessages will work regardless of what your iPhone is doing, sending and receiving SMS and MMS messages requires that your iPhone be powered on and connected to Wi-FI or cellular. Your iPhone doesn’t have to be nearby, though; merely online to act as a relay for the SMS/MMS messages.
Note that this limitation doesn’t apply to an Apple Watch on a standalone Family Setup configuration, as that has its own independent cellular number. However, paired Apple Watches shared their cellular number with an iPhone, which is why this works a bit differently.