Spotify's new UI and Library is their way of allowing you to "find your favorite music faster" and to provide a "better listening experience for everyone".
Except clearly not everyone, since you're not the only person to hate this change.
The first complaint about not being able to list your entire library by artist or to list all songs was made back in February when it was released to a small group of beta testers. When they mass released it in June to everyone, the feedback was intensely negative here on the Community page, and on Reddit, Twitter, YouTube, and plenty of news sites/blogs, etc.
And like you can see with the "Rock Star" responding here with the standard canned message of "this is an improvement, you just need to learn how to use it", they are clearly out of touch with actual users, and are trying to force you to find and listen to music the way they think you should.
The "Rock Star" Billy-J says they going to continue to build on it based on our feedback, but every post so far on the Community page about this has been listed as "Not Right Now" or some other tag that basically says Spotify is not interested in returning the basic functionality that every music library has. They've been getting negative feedback about this since February, and even more since it was released to everyone in June. There are zero indications that they're going to fix anything.
And somehow Spotify seems to not recognize that Following all artists is a poor substitute, since it negates the ACTUALLY good idea of being able to sort or filter your library by favorite artists.
Here are two recent threads where people express your same frustrations:
https://community.spotify.com/t5/Live-Ideas/Your-Library-Bring-back-Artist-page-that-contains-saved-...
https://community.spotify.com/t5/Live-Ideas/Your-Music-Automatically-follow-artists-whose-songs-are-...
As a result of Spotify repeatedly insisting that this is not worth changing, I implore you to do as I did and cancel any Premium subscription you have and move services.
Speak with your wallet, they have zero incentive to change if they keep getting paid.
I want to stick with Spotify, but to make finding my music more difficult through one of the most confusingly poor decisions ever, that doesn't deserve my fiancial support.