Notifications via internal wifi?

I have the Companion app on an Android phone. I have that app set to both my internal HA URL, and my Nabu Cassa URL. I have automations that send notifications to that device. I noticed that it was using my 500 daily allowance, which should not be happening, as the have set the notifications to send at a different rate when at home vs away. It appears that with my new phone, it is not receiving notifications via my internal network.

In order to test this, I have set my phone so that it has not got mobile data, and cannot access the internet through my wifi, it can only get to the local LAN. I can use the companion app to connect to the local HA instance, and to turn off/on lights etc. But if I try to send a notification to my device, it does not arrive. Indeed, the notifications are going via Nabu Casa instead of staying in the local network. This is a new phone. On my old phone, when I was home, notifications stayed in the LAN, and did not use up my 500 notification limit.

What should I look at to see why Home Assistant is now sending notifications only through the internet?

Thank you

The only way i have found for Companion app to use local LAN for sending messages is to turn off the Nabu Casa option in the Companion app. But that is not ideal to have to do that manually every time I leave or arrive home.

There is a related bug in Home Assistant Companion app. I had my local wifi AP set as the local wifi ap, which I think should have triggered it to start communicating internally via lan. I went into Companion App > Clicked on the home server > Chose “Home Network Wifi SSID” and added my home network wifi ap name again manually. That worked, and my ap name is in there twice separated by comma, but if i try to open that setting, it crashes home assistant every time. I had to uninstall and reinstall Home Assistant companion app to fix that.

This seems to be fixed by:

Companion App > App Configuration > Home > Persistent Connection > Always