If you have an iPhone then you should be able to run the Companion App on your iPhone and use it to sync with Apple Health. You just need to make sure it’s on the same WiFi as your Apple TV and syncs up into game mode so you can see the map where you’re riding.
Agreed. You should be able to connect the ZCA to Apple Health. However this capability seems to have been dropped from ZCA (I do not see Apple Health in Settings → Connections and have not seen data uploaded to Apple Health for more than a year. Now that Strava killed uploading of 3rd party app data to Apple Health, Zwift really needs to get this functionality working again.