Well, that explains it. You are searching in the iTunes Store, not on Apple Music. The iTunes Store is a separate entity from Apple Music. Go to any tab other than "iTunes Store" and search for music then (just make sure you are searching in Apple Music, not in your library).
I'll try to add to the explanation for adding Apple Music to your collection with iTunes.
It has been a very frustrating experience and I still find myself clueless at times as to what step is next.
So, lets say you were in "For You" and Apple recommends an "Intro to..." playlist and you liked the playlist so much you make a note to add the artist's collection to iTunes later in the day.
So, you go to Your Music, click on the search box, type in the artist in question, then in the search field select "Apple Music." Once you search it will take you to results and the best bet is to select the Artist's page. Then, in their page, you'll see Top Songs, Top Albums, All Albums, Videos, etc. Select All Albums and then if you "hover" over the album in question it will show the play button on the bottom right. Click anywhere else and it will take you to the "page" for this album. Once on this page, you'll see a "+" sign on the top right area, click this and it will add all "available" tracks in the album to your own collection (in the cloud, not a download).