@Damir It is not possible to prevent another app from playing audio. What is possible is to mute other apps when ST3 is playing but when you switch to another app while ST3 is playing the other app can always either play together with ST3 or stop ST3 playback and play its own audio.
@John Your approach will not work simply because background music needs to be played with a much lower volume than your backing tracks. The volume sliders in apps like Spotify or Apple Music only control the device volume. Either background music will be too loud or the playback will not be loud enough.