I upgraded from a series 3 to an SE. While trying to pair my brand new SE to my iPhone 13 Pro, I too received the message stating the update required for pairing could not be completed due to not being connected to the internet. I was very much indeed connected and I tried different Wi-Fi connections and all other sorts of recommendations found in the many pages of this thread. What finally worked for me is this: upon receiving the above mentioned message of not being connected to the internet, I left the message up (as in I did not select either option given to try again or start over) and navigated to the Bluetooth settings in my phone. One of the connections listed was “Apple Watch.” Clicked on the “I” next to it , clicked “forget this device” and then went back to the watch app, clicked “try again” and the update initiated. I now am paired with my watch and enjoying the new product. I hope this helps someone.