Notifications go through Google Firebase servers. This is documented here: https://companion.home-assistant.io/docs/notifications/notification-details/. Your HA server sends the notification to Google, which then sends it to your phone. They don't store the notification they just relay it.

Most mobile apps do something like this. One reason is to improve battery life - your phone can have a single connection to a Google server instead of every app needing its own separate connection.

There used to be a way to use local notifications (meaning you have to be on the same network, either locally or via a VPN), but I can't find the setting any more so maybe it's gone now. (edit: this is still possible)

https://ntfy.sh should do the trick

https://docs.ntfy.sh/examples/#home-assistant

You can use telegram integration to do that. Link.

I don't know this for sure, but if you installed the mobile companion app thru the Store for your platform, then the integration is probably using its push API to reach your device remotely.

I'm >90% sure notification workflows find me even when I am remote and untethered from home when I notify the app on my mobile devices.

I'm lazy and use a Discord webhook to a special channel.

HA mobile application opens up a notify service that I use to send notifications specifically on my mobile device HA application.

Just to add... if you don't want this, the minimal version of the HA app doesn't use 3rd party systems for notifications (you'd need to setup something yourself), so if this is a problem for you, there's also that option..

Just sayin'...

There are GSM modems that can be used by the server to send an SMS. I nearly bought one when it was cheap, but noticed just in time that the GSM level of that device was 3, which is no longer available here. And it needs a valid Sim card to work.

google. eeeww.