I don't know that this is SDK-specific, since it's true even of the sounds on the Launcher screen. but FWIW:
No sound comes out of (wired of course) headphones until the user makes a manual change to the volume (by either method). Or exits to the Launcher, or sleeps and re-wakes. (Launching an app, in theory, is a reboot—but does not activate audio. Only exiting an app will.)
And when you remove the headphones, vice versa: no sound from the internal speaker until you take one of those actions.
If it's not practical to poll for headphone insertion/removal all the time, then maybe every 2 seconds or something? Or if not that, what about this... check a) every time the user moves up/down the Launcher, b) every time any app is launched, and c) every time the System menu is opened (so toggling that button would detect headphones without fiddling with volume.)
We've got a fix merged to main, just need to get it out to y'all. Another simpler way to get the route to switch it just hitting the right d-pad button. Er, that is, hitting 
on the d-pad, not guessing the correct one. 