Airpods connect but no music
Disconnect from Bluetooth accessories (Apple):


  Open Control Center and tap [the Bluetooth icon]￼. The icon dims and your device disconnects from any accessory it's connected to, except for Apple Watch, Instant Hotspot, Apple Pencil, and Continuity features, like Handoff. If Bluetooth is turned off, you won’t be able to connect your iOS device to your Bluetooth accessories until:
  
  
  You turn on Bluetooth in Control Center.
  You connect to a Bluetooth accessory in Settings > Bluetooth.
  It's 5 AM local time.
  You restart your device.
  


It’s expected behavior that Bluetooth devices won’t connect (when Bluetooth is dimmed in control center) without one of the above exceptions.

It seems like resetting AirPods is a special case that mimics connecting to a Bluetooth accessory directly in settings, and is therefore an exception.