That's a great question! We didn't come to it yet, because we are focused only in desktop app for now. This is definitely one of the challenges we need to solve once we start working on the mobile apps. The self-hosting use case makes it tricky (and probably fun challenge to solve).

Having used several real time self hostable apps with chat (Nextcloud, Odoo, Rocket chat) this is the hard problem to solve.

Rocketchat uses it as a way to funnel you into paying. You'll get a low number monthly for free. They say 10k month but with a team of 5 people lightly using it we used that in 4 days. Or you can do it yourself, but you'll need to register your own version of the app in both the Apple Store and Play Store. For Apple apparently this is close to impossible so I didn't try.

Nextcloud runs their own server for free, but you have to accept that you'll be sending data via their server. But I've spent the last week hacking away at setting up a Nextcloud in my spare time. Got it mostly set up in a day, then the rest of the time has been trying to get notifications working on mobile. Still not working.

Odoo, I don't think I ever got notifications working.

I have researched other apps: Mattermost does something similar to Rocketchat, using notifications as a sales funnel. Element is similar to Nextcloud, they host their own free server, although I think you can self host that too.

From this experience, I would never try a new app until they have this feature solved, clearly documented, and with proof that it works and isn't a sales funnel.