Everyone I know that uses Zwift uses it through an Apple device; then why oh why no integration with the Apple Health app!!!
It works if you have a Strava account paired to Zwift & to Apple Health. Strava passes the data on if you give permission.
I use an iPad for Zwift, and iphone for health.
It looks in the health settings that you can give Zwift permission to share directly- perhaps that only works if you use the same device for both purposes.
Hope that helps