

Not entirely sure about the de-google’d version of the Home Assistant companion app, but I know the regular companion app uses Firebase (and whatever the Apple equivalent is called, I forget) to deliver notifications, and it still would using Telegram as Telegram also uses Firebase. Apprise is a bit different as it can use multiple backends. Regardless, there are multiple ways to do things. Ntfy iphone and google app do not route your data through a third party server. I self host the ntfy server on my own machine and domain and my phone connects to it and receives data. It will deliver notifications wherever I am, not just in my LAN. It also provides a nice UI akin to Pushbullet I can use to send myself stuff privately.
You can’t replicate all of what ntfy does with Home Assistant. There’s more to it than just delivering notifications, it’s the whole app frontend and persistent data etc. If it’s not clear to you what it’s for from my description you might have to go look into it yourself. Look at PushBullet, that’s most similar to what I primarily use it for.
If your purpose is long term archival you should probably be using M-Disc Blu-rays anyway, which are still actively made by Verbatim (and one other company).