The YouTube Music app appears to be testing out a new navigation, which moves everything towards the bottom of the app. Instead of having the three tabs at the top of the app, like it currently does (and even the regular YouTube app does). This is being tested among a small group of users right now, likely to figure out if it's a good idea to change the navigation to the bottom, from the top of the app. Google does periodically test out changes like this to different apps and such. Some of these changes do make it to everyone, but often times they do not.
Looking at the screenshot below, it's clear that the top section of the app has gotten much leaner, and the slideout menu on the left has disappeared. There is the YouTube Music icon in the left corner, with Chromecast, search and account settings towards the right side. It's likely that all of the features from the slideout menu are under that account settings icon (which is your profile picture, with a red ring around it). Home, Trending and Liked have all moved to the bottom. YouTube Music as also added text, which makes it easier to figure out which is which. The rest of the app does seem to be getting some minor tweaks to its design, but nothing too major.
Not all users are seeing this change, in fact the majority of them are not. So it's difficult to say how many are in the testing group for this update. It's also tough to say when this update will be available for everyone. It's possible that this update never makes it out to everyone, or it is slightly changed before it rolls out to everyone using the YouTube Music app. It's a stark departure from the design of Google's other apps, including YouTube itself. Where the navigation is all at the top. The bottom-navigation bar is something that is typically seen on iOS apps, and those that are just ported over to Android. But it could be a change that Google starts implementing across the platform.