Apple has not at all made this clear, but you CAN browse through and stream your entire icloud music library on AW 4.1, as well as asking siri to play anything else in Apple Music. Anything not synced already will stream (via BT data, wifi, or LTE).
If you are an Apple Music subscriber, this is like having all your Music on the phone back again... IF playing through the watch.
The Now Playing app will control music and whatever (podcasts) coming directly from iPhone that are or are not part of Apple Music, but you can't browse anything.
And if you don't have Apple Music, and just use the "Music" app on your iPhone to store your own stuff, you're out of luck. It will only show in "now playing".
Point is you KIND of get what you used to now with 4.1 on the AW Music wise, except the AW is the "client" to Apple Music now, not the phone. It works well, and you get all the music you want.
The problem is if you want to listen and play explicitly through the PHONE, but browse and control on the watch - you can't. You can only control whatever is playing on the phone that moment via Now Playing.
To fix this, the Music app needs to change. Apple just should have had a toggle like before... watch or phone, in Music on AW. "Watch" mode would be what it is today, which is a fully watch based Apple Music client, and "phone" would be the same, but browsing and playing via the phone (like a remote control).
Essentially, what Apple did instead in 4.x is remove the browse & remote control to music on the phone, relegating it to only control in Now Playing, and made Music on the AW a fully functional streaming Apple Music client.
Nice, and 4.1 is much better than 4.0 in that regard, but it's a very confusing paradigm. Let's hope they fix it, by adding in what was there before (in 3.x) on TOP of the new 4.1 AW-based Apple Music streaming client.
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...But now comes the dumb part. When i stream with my iPhone connected and the title is saved offline on the iPhone it will still stream the song with cellular. So instead of just loading the song from the iPhone to the AW it is downloading/streaming it with cellular connection ot the iPhone and then the iPhone transfers the data with BT to the AW. What a waste of battery and cellular data.
I'm not seeing that. If I am playing music via the phone and now playing, it plays via the phone. The AW music app isn't involved. If I am playing via BT to headphones connected to the WATCH, then yes it's an independent Apple Music client, and it will do whatever via the watch depending on what has been synced to the watch or not. This is regardless of where it is getting its data from - wifi, LTE, or yes, the iPhone that has that song on it. The iPhone is just the data connection for the watch in this case.
Only "Now Playing", for better or worse, controls the phone's Music from the Watch. This can sometimes set up a bizarre case where the watch AND phone are toggles in Now Playing, each playing different music. Or even the same track!
They need to do what I suggested above and add the browsable iPhone remote control mode back to Music on AW.