Well this has happened on both iOS 12.4.1 for our iPhone X and iPad Pro. With the Sony WH1000M3 and the Apple AirPod, if you connect it to an iOS device, then you will see the phone connects, but when you try to play music, the magic output button doesn’t show the Bluetooth headset.
Instead, even if you turn Bluetooth on and off, it still won’t work. The only thing that does is to power cycle the device.
See https://www.howtoisolve.com/ios-11-bluetooth-not-working/