“Sir, you’ll need to add a new line of service to your AT&T account in order to activate your replacement Apple watch. You will get a new telephone number.”
That was the response I got from AT&T’s customer service regarding my AT&T cellular plan after I replaced my Apple Watch under the AppleCare+ Express Replacement. I followed Apple’s guide here and it bombed out under the “Transfer your cellular plan to a new Apple Watch” section. https://support.apple.com/en-us/HT207578
I knew something was wrong with that because I was simply transferring my AT&T phone number on my Apple Watch to my new Apple Watch. It took two Customer Service Reps and 1 hour 43 minutes of my time to get this figured out but I finally was escalated and spoke to a competent CSR at AT&T.
What this boiled down to was an EID update on AT&T’s servers with my new Apple Watch’s EID. Although AT&T says you can do this self-service style, you can’t (at least as of this posting). You can see where I tacked on my issue to an existing thread: https://forums.att.com/conversations/apple/accidentally-deleted-esim/6342d7877c2ab96af9f1cbb0
AT&T’s self service portal for updating your Apple Watch eSIM is broken… or non-existent. If you replace your AT&T Apple Watch with cellular, you’ll need to call AT&T’s customer support and tell them “I’ve replaced my broken AT&T Apple Watch and I need my new Apple Watch EID updated on my AT&T account so that I can add my existing AT&T cellular plan.”
Once AT&T updates your EID, reboot your Apple Watch and close the Apple Watch app on your iPhone. Restart the Apple Watch app and you should be prompted to add the AT&T cellular plan, inactivated mind you. Once you see the cellular plan as available but inactivated, go through the process of activating the cellular plan on the iPhone Apple Watch app. Once it is activated, reboot your Apple Watch again and wait 5 minutes. You should then be able to make and receive cell phone calls.