You must not be in the United States. Here, regular home cable/fiber internet ISPs usually assign a (dynamic) public ipv4 address to your router. Your cellular internet connection is usually behind cgnat, both on your phone and the new home wireless internet from the cellular providers, but regular home cable/fiber internet is the most common home internet type.

So I agree that the watch would likely be behind NAT (for IPv4), I just disagree with the statement that ISPs usually put their customers behind cgnat.