Apple Watch with cellular
Why can’t I send sms text messages on my Apple Watch?
Apple Watch
From https://support.apple.com/en-us/HT205547
1. To receive SMS, MMS, or push notifications from third-party apps on your cellular Apple Watch, your paired iPhone must be powered on and connected to Wi-Fi or cellular, but it doesn't need to be nearby. You also need to be signed in to iMessage on your iPhone.