OK, I think I have it working…
I did a search on the internet, and someone said that, according to Garmin Support, you have to have a seed bike ride recorded on your watch for this to work. That is, you have to track a bike ride outside, or track an indoor bike ride.
So, at lunchtime today, I set my watch to transmit my heart rate to Zwift as usual, but also tracked my indoor bike ride on the watch. In Garmin Connect, this gave me two activities - the one from the watch had time, heart rate, calories etc., and also had Training Effect (it didn’t have any power data).
The one from Zwift had all the data from Zwift, including power data, but no Training Effect.
This evening, I did the same thing with another ride on Zwift. Again, I had two activities in Garmin Connect. The one recorded on the watch was the same as before. However, now the one from Zwift had Training Effect data - Primary Benefit, Aerobic, Anaerobic, and Exercise Load.
So, that looks like it’s working. Tomorrow, I’ll try without tracking the ride on the watch, and see if it still works.