Was a pain to setup, but finally it connected! Didn't test any notifications yet, but phone asked if I allow sending them, so I think it should be ok now.
Had to restart an app, reboot headset, removed pairing from Bluetooth settings twice on both devices, finally connected. Before that, it found the iPhone, but went "Connecting..." and then timeout.
iPhone X, iOS 13. Oculus Quest latest firmware. Have all experimental features enabled. Set this up using hand tracking!
Will update later whether the notifications show up