In a rather interesting move, Google has recently launched the YouTube Music app for Apple Watch. However, you do need to be a YouTube Premium or YouTube Premium Music subscriber in order to utilise it.
Among the main function of the app is allowing users to browse their music collections and song recommendations directly from Apple Watch. Users can also add YouTube Music compilations into their favourite watch face.
Users can also utilise the Apple Watch app to cast music from their phone to other devices. Naturally, they can also control music playback through it, although users are still unable to stream YouTube Music directly on Apple Watch.
According to Google, the app is compatible with Apple Watch 3 and newer versions that runs at least on watchOS 6. Available immediately, you also need to install YouTube Music app on your iPhone as well.
(Source: YouTube Official Blog)