Minos doesn't run a notification server for you.
A native push would have to travel through a gateway that the app's publisher operates — the exact kind of middleman Minos is built to avoid. So notifications ride a channel you control. The common choice is ntfy, a free, open-source notifier you can self-host or use at ntfy.sh, with its own iPhone and Android apps.
The message your relay posts looks like this:
curl -H "Title: New PR · owner/repo" \
-H "Click: https://minospr.app/pr/owner/repo/7" \
-d "#7 fix the thing — by author" \
https://ntfy.sh/your-private-topic
Nothing here touches a Minos server. The webhook lands on your relay; your relay posts to your topic; ntfy delivers to your phone.
Your git host already emails you on pull-request activity, with no setup at all. Notifications are for when you want a tappable alert on your phone.