Apple has been developing a Sleep app for the Apple Watch, with an App Store listing for the Alarms app revealing Apple's as-yet unreleased app.
Appearing in an App Store Preview listing for the Alarms app, a screenshot for the app shows a page for managing "Sleep," with users able to enable or turn off a "Wake Up" alarm. The text below mentions users can "Set your bedtime and wake up in the Sleep app," something that has yet to exist on the Apple Watch.
Currently, the Clock app on iPhone offers Bedtime, a feature where users can set when they want to wake up and how much they want to sleep, and to receive reminders on both their iPhone and the Apple Watch when it's time to sleep. The app also performs sleep tracking functions.
It is currently not possible to manage the Bedtime feature from the Apple Watch, aside from dismissing the sleep notification. The listing found by MacRumors certainly suggests the ability to enable and disable the function from Alarms, but doesn't directly say if the Sleep app is on the Apple Watch or the iOS device.
Given the ability for Apple Watch users to install apps directly to the Apple Watch via a watchOS version of the App Store, it is plausible Apple could update the app via that mechanism instead of awaiting a watchOS update. At present, the Sleep app isn't in the watchOS beta currently in testing.
While rumors have suggested the Apple Watch will include sleep tracking functionality at some point, including "Time in Bed tracking" under the codename "Burrito," it has yet to make an appearance in watchOS itself. Users wanting to perform sleep tracking either have to use apps within the Apple Watch App Store or a separate system entirely, like the Apple-owned Beddit.