I'm not sure what best practices look like for web / mobile push notifications, and it will probably look different on different platforms. For now, we can probably get away with the client periodically polling /ping with a cursor or something, and sending notifs if anything new has been found.
Ideally, the appview would do all the calculation of whether a notification was sent, since it's more of a long running service, but obviously the client has to get involved at some point.