It was inevitable that Google's music streaming service would be video-focused once placed in the hands of YouTube, but plenty of folks interested in music have zero interest in watching the associated video. Thankfully for them, The YouTube Music app now lets you seamlessly switch between music videos and plain 'ol music with a single toggle, and you can even disable videos entirely by default.
GIF showing off the new toggle (visible at the top of the inner screen about halfway through).
The transition between the video and standalone music are supposed to be "seamless" — at least, for the ~5 million tracks that YouTube claims to have "perfectly time-matched." The toggle will appear at the top of your screen while playing music, allowing you to switch between a "song" and "video" mode. A separate toggle in the app's settings lets you disable music videos by default.
When switching between video and music, your position will now sync between the two formats, placing you further in if you switch to a video and it has something like a long exposition or introduction before the music actually starts. In essence, that means if a given segment of a song (say, a minute in) corresponds to some other point in the video (say a minute and forty seconds in), it will jump you between those relative points when you switch formats.
Song -> Video toggle visible at top. Prompt to disable videos by default on bottom right.
The latest version of the app I have installed (3.23.52) appears to have the new feature. It isn't clear if it's rolling out based on a server-side change/flag or if it's tied to the latest update, but you can try your hand yourself over at APK Mirror if you don't see it.
The option to play songs instead of music videos by default in the app's settings.
YouTube Music may still not have access to your uploaded tracks from Google Play Music, but at least you don't have to put up with the derpy video-first focus anymore if you don't want to.