So I looked into this a while ago, but also once again after your request. This verdict is that adding support for YouTube Music will cause way more problem than would solve.
Here are the pros and cons.
Pro:
Granular quality control. Users will be able to select specific quality to play.
Cons:
Unnecessary code complexity. YouTube Music loads differently enough from YouTube that just adding the url will not work. I will need to add a parallel loading logic to my script.
Limited usefulness. This script will only be useful if you choose to play the video verison of Music. At that point just playing on youtube.com would achieve 99% of the same results.
Negative impact on user experience. YouTube Music actually remembers the video quality you set even though it does not provide a way to do so through its UI. This means if the script breaks or if a user chooses to uninstall the script before reverting to "auto" quality, playback would be stuck with the quality that was previously set. And this persists across reloads.
Lack of premium bitrate. YouTube Music lacks the possibility for video content to be loaded with premium bitrate, making a major feature of this script unusable.
Pls add support for Youtube Music. You only need to add the url.