Is it possible to completely remove the before/next buttons from the CPNowPlayingTemplate?
I've already tried to set live-streaming mode, but the buttons are still there.
You can disable the next and previous buttons, even outside of livestreaming mode, to cause them to render as disabled as in your screenshot above.
It's not currently possible to hide those buttons, but that's not unique to CarPlay - even disabled, the next and previous buttons show up in the now playing widget in Control Center and on Cover Sheet. Please file a feedback radar with more details about your use case and why you'd want to hide them. Thanks!