It is possible to listen to music from your iPhone via wired headphones (controlling playback on your Apple Watch), but not to listen to music from your Apple Watch via wired headphones.
Under watchOS 4.x, for controlling playback of music from your iPhone rather than the synced playlists on Apple Watch (for which Bluetooth headphones or a Bluetooth speaker are required), then - other than by using Siri - it is necessary to first start playback on your iPhone before being able to control playback on your Apple Watch.
When you are already playing supported audio on your iPhone (whether via the Music app or a third-party app), the Now Playing app is shown automatically in the Dock on your Apple Watch and can be used to control playback on your iPhone. However, unlike under prior versions of watchOS, those controls no longer include the ability to browse or select playlists via screen-based inputs.
Now Playing can be configured to be shown automatically on Apple Watch upon raising your wrist when playing supported media on your iPhone. This is the default setting. To turn this feature off or on:
On your iPhone, in the Watch app, go to: My Watch (tab) > General > Wake Screen > turn off Auto-Launch Audio Apps.
If desired, Now Playing can be added to the Dock permanently and/or added to a watch face as a complication.
Follow the instructions here:
- Listen to music on your Apple Watch - Apple Support
- Now Playing
- Play music
- Change your watch face - Apple Support
- Use the Dock on your Apple Watch - Apple Support
If the Music and/or Now Playing apps do not offer all of the features that you would prefer, then you can submit a feature request to Apple here: