For now, the web option has all of the sections offered in the app: Library, Search, For You, Browse, and Radio. It will have access to playlists as well as searching and playback of a user’s library if Sync Library is enabled. More features will be added to the web model over the course of its development.
It’s a long wait for a web listening option from Apple. Other rival platforms including Spotify and Pandora have long had this choice available to their listeners.