Make the Artists and Albums Tabs under music drop down menus with the option to sort by either followed artists, or saved artists (now liked artists) for the artists tab and liked albums, and saved albums for the albums tab. What I mean by this is have the Albums and Artists tab show all of the artists that you have songs from, OR the artists you've followed or albums you have specifically saved.
To clarify, for both tabs, have the option of viewing artists or albums from which you have saved music, as the old albums and artists tabs function, or artists you've followed or albums you've specifically saved, as the new artists and albums tabs works.
This will return the functionality of the artists and albums tab that was lost with the new update (I have 3.5k songs, but artists now only shows 8 artists, and I have no way to sort through artists from songs I've saved) without forcing you to conpletely remove the followed artists and saved albums tabs you implemented in the new update.
Updated on 2019-07-16
It sounds like what you are trying to do is already possible.
You should be able to drag down a playlist to reveal a filter where you can sort the playlist. In this menu you can choose to, for example, to sort according to Artist or Album. Take a look at this page if you'd like to know more about how the new library works.
Let us know if this is the feature you are looking for.