Why does iPhone Activity not recognize Apple Watch Activity has been set up?
I have since solved the problem. Something was seemingly corrupted in the iPhone's Health database. Nothing could read or write data to the Health database, including step data (which should be automatically added from the Mwhatever chip) and manually entered data such as weight. 

To solve the issue, I unpaired the phone and watch, then set up both the phone and watch as new. Setting up the phone from a backup did not solve the problem because the (hypothesized) corrupt database was (seemingly) included in the backup.

Since setting up the phone as new and re-pairing the watch, Health data works fine.