Hello, I'm having the same problem and hope you can help me. I can't choose the silent notification style and only have the "show notifications" and "playback" options shown. It wasn't like this earlier and I didn't update my phone.
Im sure by now you might have figured it out. If not, on the home screen, slide down, press the section displaying current song for about a second or two until you see playback options. Just select silent option and done! 👍🏼