Microsoft have pushed an update to the iOS version of Groove which includes some of the UI changes. On the Windows app Microsoft simplified navigation on of the app a few weeks ago and now the iOS version has the same change with albums, artists and songs all now grouped together under My Music.
You can find the app in the iTunes Store.
What’s New in Version 11.0425.1313
Albums, artists, and songs are now grouped under My Music
Simplified app navigation makes it easier to find recently played music
Various bug fixes