Modem firmware is, but the Linux running on the modem isn't. It's under GPL. Some people would even like to run mainline Linux there, eventually.

Even the userspace running on the modem can hardly be called completely proprietary. It's some busybox system + bunch of other tools that are also under GPL or other OSS licenses. I didn't measure it exactly, but it wouldn't surprise me if the amount of proprietary code in userspace of the modem is < 20%.

The fact that the firmware contains GPLv2 code doesn't mean it's not completely proprietary.

You can't modify the modem firmware and then still legally operate it in public networks under most legal jurisdictions around the world.

Sure I can. Modem's firmware is split into two parts. Linux OS running on ARM CPU and modem's modem FW running on hexagon cores. It's possible to modify ARM CPU code without affecting modem's operation much at all. ARM CPU just takes care of some audio/USB and such interfacing tasks. It's laregely free to run your own tasks. The manufacturer even allows customers to build their own userspace code for the ARM CPU inside the modem and extend it this way as part of quectel open linux SDK.

Anyway, the original issue was about notifications, and ability to implement them without consuming too much power. And one of ways to do it is to extend the modem this way.