Is your Apple Watch telephone number listed on your iPhone in Settings-Messages-Send & Receive?
No and it is not needed there. It also looks like you are magical by having T-Moble and AT&T Wi-Fi at the same time. It also appears that your Watch's phone number does not have a "Check" by it to show it as active. So it really serves no purpose.
Dave
No worries and the site is wrong in their suggestion. Think for a moment, how would your Watch be able to send an iMessage by using your AppleID if it did not already have an LTE signal in their example.
Now on your specific question: it seems like you did not have a good LTE connection. What showed on the Control Panel or the Explorer Face?
Dave