I nearly always have music playing in the background while in focus mode, and, typically whenever I need to pause working on the task at hand (e.g., someone has dropped by my office to talk to me), it also means that I want to pause my music. Likewise, when I go to resume my task in focus mode, I want my music to start playing as well.
I personally use Spotify 80% of the time for background music, but my thought is that this could be as simple as having the option to trigger a play/pause keyboard input when the play/pause button on the focus bar is pressed, which I believe would work with most desktop audio apps. This would avoid the complication of having to build a specific third-party integration for each app.