Thank you for reaching out here in the Community!
As you've noticed, in order for an artist to appear in the Artist tab in Your Library, you need to select FOLLOW at the top of their artist profile.
If it comes to the liked songs page after clicking on the artist's name, there's an ongoing issue created and the right team is currently investigating this.
If that's something you're experiencing, make sure to add your +VOTE there and subscribe to the topic. That way you'll be notified with all the future updates on that case.
For now, I can suggest that you go to your Liked Songs and use the Filter option to search for the artist you want to listen to. It will display all the songs you've liked by a specific artist.
If you you'd like to see a certain feature (new or old) on Spotify, you're always welcome to submit an idea. For more details on how to do it, make sure to check out this Spotify Answer.
I hope you'll find this info helpful!
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Note: I'm not a Spotify employee.