I haven't said anything yet, but an AltRant notification server exists. Support for it will arrive very very soon on the AltRant app. It will run locally on the end user's personal computer, and it does not require a constant connection to the phone. Both devices need to be connected to the same local network on first connection, but after that you can wander out of your house or disconnect from the local network and still receive notifications.

DISCLAIMER: ALL SENSITIVE USER CREDENTIALS ARE NOT STORED *ANYWHERE* EXCEPT ON THE LOCAL USER'S MACHINE. NO DATA IS SENT TO ME. THE SERVER IS OPEN-SOURCE, HAS NO RELEASE BINARIES AND RUNS ON PYTHON.

Note to @dfox: if you want this to not exist or not be supported inside AltRant, please tell me or send me an email about it.