I understand your frustration with these changes. Here is a page that goes over the changes and how they work.
I believe you are probably expressing frustration specifically with the artists tab on this post, right? With the update, the artist tab now only houses artists you're following (which you can sort alphabetically), and then suggested artists underneath. It won't have artists there that you have songs by in your "liked songs" but do not follow. If you would like to mass-follow all the artists you have songs by, you can find a tool in this thread to help with that.
I realize this is not the exact functionality you're looking for. I do hope it helps somewhat, though.
This is Spotify's new way to allow 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.
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.
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: