How do I turn off the music?

Tap on the "Pause playback" button:

Play music on iPhone - Apple Support

Close the Music app and the music should stop. Depends on the device you have on how to see your open apps. For more specific on individual apps, google search: how to see what apps are open in iPhone XR, iPhone 7 Plus, Mac OS - Big Sur etc.

you don't give too much info...so I do not understand what is actually happening...your phone always plays music? Your laptop plays music? iPad?

Go to your settings, Music, then toggle OFF the SYNC Library. this will prevent it from automatically looking for your library/content and will not sync across all of your devices.

Also, you can go to the CarPlay settings...

Settings, General, CarPlay....select your car.

Then customize the order. You can maybe move Music to the bottom of the list

This isnt good enough. I am sick and tired along with hundreds of thousands of like iphone users of the music automatically playing as soon as it connects to bluetooth or when I try to play a tik tok video over bluetooth it CONSTANTLY tries to (successfully) usurp the connection. TIRED OF IT!! MAKE A WAY TO TURN OFF AUTOPLAY OR I WILL CANCEL MY SUBSCRIPTIONS. NOBODY ELSE FORCES THEMSELVES ON MY CAR LIKE YOU. AND DONT GIVE ME THAT “PAUSE IT” BULL