Amazing how such a simple thing remained undiscoverable. . . simply because I did not realize there was MORE to the page that I previously had used to start music PLAY.. . "swipe up" was the key clue you provided, but then I STILL missed it initially! I swiped up FAST and was taken to "flashlight" and other utility controls. By accident or just luck, I suppose, I gently swiped up and the two side by side buttons for SHUFFLE AND REPEAT were revealed, but EVEN then! . . . I had a problem figuring out the final clue I needed to understand how these buttons, themselves, functioned. Each "button" is surrounded in red if selected and just surrounded in screen white if NOT selected. It is possible, however, to have BOTH buttons selected, so both are surrounded in RED. . . If you don't use them much and have not been to this screen much. . . with both in red background, it looks as if THAT is the normal position.
So, rather than being the interface of choice where usage is obvious, this layout camouflages the buttons and their functions. Maybe the WYSIWYG gurus need to revisit Apple music folks! Where is the Woz!
OK. I get it now. . . but in 6 months?! GEEEEZ.