The Moto 360 supports sleep tracking through a third-party app called “ Sleep as Android.”
The app is not in-built in the watch, but it is compatible with it. It can be downloaded through Wear OS on the Google Play Store app. For the sleep tracking app to work on the device, it must be downloaded on the phone and the watch. The “Sleep as Android” app performs various functions, including REM phase detection.
To learn how to use the app after installing it, you can read this article: https://sleep.urbandroid.org/documentation/getting-started