I can't send any shortcuts to the Music app. I tried with a button on the Touch Bar and again with a global keyboard shortcut, and the app won't recognize either.
I'm trying to create a dedicated Play/Pause button on my Touch Bar but I tested this problem with other shortcuts and none of them worked. I used "Send Shortcut to Specific App".
On the action page, not the trigger page, there's a checkbox that says "Bring app to front before sending" and another below it that reads "Immediately switch back after sending"
It must be the action you have selected. I can see it when I select "Send Shortcut to Specific App". I assigned a shortcut to play/pause Music using the Keyboard section in System Preferences. Then I send that shortcut to Music using BTT and the Touchbar.