After multiple attempts and too much wasted time trying to update to 7.0.1, I give up.
Unpairing via the phone, resetting from the watch, restoring from backup, setting up as new, fresh reboots; it made no difference.
I don't store anything on my watch, and since it added a native calculator, not even PCalc, so no non-native apps.
Every attempt started with 3.7GB free, which should be more than ample for a paltry 91.7 MB update. But it would fail just past half way every time, and said it lacked an internet connection. Not according to my router, which showed both phone and watch had pulled IP addresses.
The cherry on top -- it refuses to restore from backup now.
Addendum -- if the "null" error appears when trying to restore from backup, there is a way out -- skip the visual pairing method, and use the manual process, with the six-digit code. It will restore from backup that way.
Miserable failure for a company that prides itself on the UX.