I use the Apple Music app constantly and never get nagged to buy the service. On macOS, I just unchecked the "Apple Music" checkbox under "Show" in the Music Preferences, and on iOS turned off the "Show Apple Music" toggle in Settings > Music. Boom, no nagging.
Opt in vs. opt out. Those check boxes should be disabled be default. And they are not.
Tbh I don’t think I’ve ever used the new Music app (I’m on Spotify) and the last two are not available where I live :)