I have a similar setup, prometheus and grafana (alertmanager is a separate thing from the normal grafana setup, right? I'm not even using that), and I use discord webhooks for notifications to my phone (I just @ myself or use channel notification settings).
Even a quick Prometheus + alert manager setup with two docker containers is not difficult to manage - mine just works, I seldom have to touch it (mainly when I need to tweak the alert queries).
I use pushover for easy api-driven notifications to my phone, it’s a one-time $7 fee or so and it was money well spent.