A10 built-in sound doesn’t play when it auto-switches from music mode

I fall asleep using sleep meditations from iOS Music, with my A10s set to switch to sleep mode once they detect I’ve fallen asleep. I have the rain sound set as my built-in music, and it plays if I manually set the earbuds to sleep mode.

However, when it auto-switches while I’m asleep, the built-in sound doesn’t play. Most nights, I wake up soon after I fall asleep to silence. If I double tap the left earbud I hear the notification that it is switching to music mode, so I know the auto switch happened. If I double tap again, it switches back to sleep mode, and the rain starts playing.

The problem, of course, is now I’m awake again. Why doesn’t the built-in sound play when the buds auto-switch to sleep mode?