You can avoid most of the annoyances by always using the Songs view and hitting Command-B to get the columns browser like iTunes. Then edit the columns to browse in the menu.
That's a neat trick! I just wish there was a Playlist option and Favorites. (The "Groupings" component is empty for me, not sure if that is supposed to have the playlists)
For playlists you can choose “view as songs” in one of the menus and then enable the column browser. I have a smart playlist for the classical genres that I do this for.
The groupings is a tag that’s free-form text: one nice thing about Apple Music is you can edit the tags, even if you don’t buy the music. I typically split “Classical” into “Baroque”/“Classical”/“Romantic” and then rewrite “composer” to be “last name, first name (years of life)”