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.
This would kill bridges like slidge. They authenticate to WhatsApp using the web interface and that token lasts about two weeks before you have to relink it. A limit of six hours would make it unusable.