how do I seek in itunes store
how do I seek a specific artist in itunes store
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The only way I've found is to search for the artist name or a song by the artist using the search bar in the upper left in your library. Then look for the artist's name in the results under the "Albums" section, or the "Artists and more" section towards the right of the results. Click on the artist's name, and it seems to do a search for that artist just as iTunes did.
You can also use Safari by going to duckduckgo.com, and searching for "Apple Music" then the artist name (e.g., "Apple Music Morphine"). Then click on the "View on Apple Music " button in the results, which will open Music.app and search for the artist.
Unfortunately Music.app has managed to become less intuitive and less capable at the same time (subjectively). Here's hoping for an update before people switch over to Spotify just for the UX, which does allow searching by artists.