It might be not this simple in case of notification providers, the notifications are somehow sent in the name of the app I guess. And don’t forget: in general, this principle is true for most of your apps that send notifications. I.e. if you are getting Signal or Facebook notifications, it uses the same principle.

Btw, google is not the only notification service for android. Check up on Unified Push, there are many alternatives to do this, and there are some apps that support these alternatives in their non-play-store builds.

In general, notifications on Android don’t go through apps, that would require apps to run all the time and consume too much battery. They instead are going through a notification provider (google in the default case). This is why your notifications arrive, but you have no other connections to your HA.

Edit for clarification: HA uploads it to google servers (which of course doesn’t need port forwarding) and your phone then polls them from google.