Turns out the 1st generation (as opposed to Series 1, which came next) Apple Watch does not support the new heart rate features in watchOS 4.
Here’s how to tell what model Apple Watch you have:
- Open the Apple Watch app on your iPhone
- Tap the My Watch tab
- Go to General > About
- Scroll to the Model field
- Tap the model once — it should change to a code that starts with the letter A
With that Apple Watch model in hand, head over to this Apple Support page, which will tell you which series your Apple Watch belongs to.
The two original Apple Watches were models A1553 for the 38mm case and A1554 for the 42mm case. Those are the two models that won’t support the watchOS 4 heart rate changes.