No internet connection when updating
First check you have no other sports watches like Fitbit that are paired to your iPhone
Try again, if no luck
Try and force restart the watch. i.e. press and hold both the side button and Digital Crown for at least 10 seconds, then release both buttons when you see the Apple logo.
Then Force Restart the paired iphone m
Force restart iPhone – Apple Support
Then in the iphone, Settings, General, Transfer or reset iphone, Reset, Reset network settings.
Make sure you have no VPN or VPN based adblocker
Then reset the router to factory settings which usually involves a paperclip on a little hole.
Try again
I recommend reviewing the steps in the articles below
How to pair an Apple Watch with your iPhone
Click: How to pair your Apple Watch with a new iPhone - Apple Support or
Can’t pair an Apple Watch with your iPhone
Click: If you can't pair an Apple Watch with your iPhone - Apple Support or
Apple Watch not paired with your iPhone
Click: If your Apple Watch isn't connected or paired with your iPhone - Apple Support