I run a prosody server and have a couple of users who run Monal, and notifications work reliably for us!

I made sure to follow the considerations for server admins and it’s been ok.

Regarding the push service: unless you deploy your own version of the app, it’s not possible to self-host your own push service. The flow looks like this:

XMPP server -> Monal pushserver -> Apple pushserver -> Device

Apple only allows the developer of the app to send notifications to their push server. They enforce this by giving the app developer a key specific to their app.

The linkage between XMPP server and Monal pushserver gets set up by Monal: when it connects to the XMPP server, it instructs it to send messages while it is offline to the Monal pushserver.