The only way that you will be able to integrate your Nest products into SmartThings is with the custom NST Manager SmartApp. (It’s the only option you have)
As for doing anything with motion, if you are running the REST streaming version of NST, it may be possible with webCoRE to run a Piston on motion event captured and then some action to get your music playing. Haven’t done anything with that. (I am doing something similar thru IFTTT where on receiving a notification event for motion from the Nest Application, I turn on a virtual switch in SmartThings and when that switch turns on, I am sending an audio notification to my Bose speaker via webCoRE to alert the intruder to start running).
Start with getting NST Manager installed first and then you can figure out if you can do something with your music later.
Moving forward, for all your questions / issues, post them in the official thread. They will be seen by more of the NST Manager customers/users in the community.