Music. When I click the Music icon. I have either my Library or iTunes. I pick iTunes, I see iTunes on the right side. But when I enter search, the iTunes screen disappears and it defaults to Library. Trying to change t over to iTunes, I can't.
My last iMac ran High Sierra. The Music icon, under High Sierra, I always thought was the iTunes icon.
Big jump to Sequoia. Still learning.
Correct. The icon in High Sierra was for iTunes and Music didn't exist, at least not on the Mac. If you're running Sequoia, the music icon is for Apple Music, which is not iTunes.
WhenI hit the Music Icon this is the screen I get below. iTunes Store is highlighted and I can get into the iTunes Store but can't search.. Under High Sierra I could use the search function, top left of sidebar and search for say Doobie Brothers, and right side would go to Doobie Brothers. But by a fluke, I found "Learn to let go" by the Doobie Brothers and it took me to their newest album and I purchased the album after putting in my Apple ID.
This is where Apple have caused endless and needless confusion: although the iTunes app doesn't exist in Sequoia, you still purchase music through the iTunes Store (which is the only bit of iTunes still remaining, and it's now part of Apple Music). Confused? Yes, aren’t we all.
When it comes to Search in Music, it should still be there? I can't run Music on my Mac (still using High Sierra), but on my iPad, the search function is listed in the Music sidebar, 3rd item down. Confusingly (again!) my iPad also has a separate iTunes Store icon which seems to be much the same as Music, though like Music there is a search bar.
Back to my original question. The search function used to work under High Sierra. When I try it now, the iTunes screen disappears, iTunes is highlighted and he screen says searching iTunes Store, but nothing happens. Does this mean I have to abandon the iTunes Store and use Spotify...of which In have no clue?. I assume there is a search function in Spotify and will songs downloaded by Spotify get added to may Library automatically?
The search in High Sierra was between your iTunes Library or the iTunes Store. Your Library now is your old iTunes Library which has been converted to Apple Music, while the iTunes Store isn't really iTunes, it's just the place where you buy music.
Spotify is an entirely separate thing. It has its own Search, and you can stream music to your heart's content, with adverts between tracks if you're not paying for their Premium service. I've never bought music through Spotify, so someone else will have to tell you about that, and what happens to the music you buy. There may be a function to add directly to your Music Library? I don't know.