Hi Christopher,
Using the Apple Watch as a HR monitor with Zwift can be a bit tricky, so I recommend following all of the steps in our KB article (if you haven’t already).
https://support.zwift.com/hc/en-us/articles/115002509406-Using-the-Apple-Watch-with-Zwift
Our team is aware of the issue of the Apple Watch staying paired after Zwift has been closed. The team is working on a fix, but in the meantime, you may have to force quit the app after use. Thanks for your patience while we work to improve the Apple Watch connection with Zwift!