I just started noticing this as well. Not a fan of Apple’s mentality these days. Always giving us something we don’t want, and no option to turn them off. Annoying. Back in the day, there was always an option to turn features off.
That being said, I tried the Siri & Search suggestion. I turned both off. But still saw the little clock icon on the top right of the Music app icon, in the taskbar. Then I decided to reboot my iPad, and voila, clock icon gone. In fact, Music app icon doesn’t populate in the taskbar anymore. Good riddance. And to test, I launched Music again, and it hasn’t come back...yet. So will see if it holds up. If it comes back, I’ll post.