Set the “Exercise” goal for the Apple Watch Activity app

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.

If you hold onto the handle bars, your WATCH has no way to tell that you’re exercising. Your arms need to be swinging during Walking activities for WATCH to credit you exercise minutes.

As @RedEagle2000 mentioned, your activity also needs to cross a certain intensity threshold. That intensity is specific to each individual, with WATCH learning your exercise capacity through your measured heart rate throughout the day, your other activities, etc. Calibrating your WATCH as per Apple’s instructions can help in that department.