How to play music on iPhone via Apple Watch on watchOS 4?
Correct, with watchOS 3.x it was possible to use Apple Watch as a kind of remote for iPhone's Music.app:

Browse all available music by artist/album/genre
Start/stop playback on your iPhone with Apple Watch
Change the music source from iPhone's storage to Apple Watch's storage


Answer
Unfortunately, starting with watchOS 4, you can't browse music on your iPhone to start playing it using your Apple Watch.
See also Apple's Apple Watch User Guide on Music/Now Playing for using Music.app with watchOS 4.


Workaround
You may want to use this workaround:

While watchOS 4 will no longer allow a user to browse their iPhone's
music library, they can still use the Apple Watch to control it. In
fact, it's now easier than ever: A &quot;Now Playing&quot; screen shows up by
default when the user is playing music from their iPhone, giving quick
access to pause, skip a track, or adjust the volume with the Digital
Crown.
However, in order to take advantage of this, users must start the
playback of music on their iPhone, then continue controlling it via
the Apple Watch.