apple watch series 6 (GPS + Cellular) text messages to non-iphone users

FYI: All SMS/MMS texting Must have the iPhone powered on and connected to the Internet. Even when you are miles away from the iPhone.

Basically the cellular chips used in the Apple Watch only talk LTE Data. They do not have the voice circuits of a traditional cell phone. Phone calls use VoIP (Voice over IP) which is data only.

But SMS/MMS texting requires the traditional cellular voice circuits. The Apple Watch deals with this by connecting to your iPhone (across the Internet if necessary), and your iPhone sends and receives all SMS/MMS text messages.

iMessage between iPhone users works because it is also a data only protocol.

As Chrisj4203 says, you should verify that your new Apple Watch is really connected to your cellular carrier's network. If it is, and you can make phone calls away from your iPhone, then make sure your iPhone is powered on and able to access the Internet so it can relay your SMS/MMS text messages.

I guess you can tell them that when you raised the question here, someone that has a Series 6 Watch says that it works just fine on his Watch, and it is activated with AT&T also. So maybe it isn't the Series 6.

Check with your cellular provider to have them check the account provisions for your Watch. You should not experience a problem with that, but for SMS, the provider needs to troubleshoot that.