WatchOS update 9.6.2 fails Unable to Verify Update not connected to internet

I have been trying (and failing) to install the 9.6.2 (and before that the 9.6.1) WatchOS update. Every time I try I get through downloading the update and make it ~50% through "verifying update" before I get an "unable to Verify update (because you are not connected to the internet" error message.

I have followed the recommendations by Apple (make sure wifi and bluetooth are enabled on both my phone and watch), tried unp[airing and re-pairing the watch several times, have tried unpairing, erasing the watch completely and performing a fresh pairing (do not install backup) multiple times. I have tried pairing the watch with a different phone and even tried installing directly from the watch Settings.

I have had apple support walk be through all the suggested methods to overcome this issue and hit the exact same failure point (at that point Apple Support basically said "your watch should now be updated" and disconnected the help session...). The watch is still stuck at WatchOS 9.6 (no .1 or .2 at the end)

No matter what I have tried, every time the install fails at exactly the same spot (~50% through verifying) with the same unable to connect to the internet.

Neither the phone nor the watch have an issue downloading the update from the internet. The phone was able to successfully download and install the latest iOS for the phone without issue.

It's almost like during the preparation phase of the WatchOS update the preparation itself disrupts the internet connection for either the watch or phone...

Any suggestions beyond unpairing/re-pairing the watch or unpairing the watch and performing a new install?