Display ephemeral notification popups. See: https://www.w3.org/TR/notifications/, https://developer.mozilla.org/en-US/docs/Web/API/notification.
This is surprisingly complicated to get working. The straight-forward examples work on desktop browsers but fail on Android phones. To get it working there you have to generate the notification from a Service Worker, an otherwise unrelated API. There's some discussion of this change here.
Also, when the first notification appears on an Android phone, it makes a loud "Bing!" sound and vibrates. Turning off the vibration is documented and works, but I haven't found a way to turn off the sound. So that's going to get pretty annoying.
On iOS, web notifications are not supported at all for now.
ACME Labs / Web APIs / Notification