The issue here is more complicated. A self-hosted Zulip server needs to send a push notification that reaches the Zulip mobile app on someone's device.

For security model reasons, those push notifications need to be sent to Google/Apple via a server operating by Zulip itself. So your local Zulip server needs to share a secret with the Zulip mobile app on your device, and then it can encrypt the push notification's content so that only the destination mobile app can read it (and the intermediaries cannot).

It's a basic cryptography problem at a high level, but there's subtle details around what metadata can be safely encrypted (the client does need to know which Zulip server's secret key to use!), backwards-compatibility, library choice, etc., that make it not trivial, which is why we haven't managed to implement this yet.