Doesn't the protocol already need to do something to support that? Presumably it's an out-of-band notification, and they needed to add support for that. If they already added FCM an APNS, they'll have to add something to support a 3rd OS. It could be in-band or out-of-band, but either way sending a message on a TCP connection is really all that is needed.
As a side note, Jabber did add an in-band way as you suggest, but then also had to add OOB signalling because Apple disallows open sockets for background apps.
Yep, it does, so you could do this; the problem for the Linux desktop is just that there isn't a standardized out-of-band push notification system yet. (I saw another commenter mention UnifiedPush, which sounds interesting - in any case it's not widely supported yet.)
> As a side note, Jabber did add an in-band way as you suggest
It's been a while since I looked into this in detail, but IIRC Jabber generally doesn't have a server-side way to determine which messages should notify? As I recall, the protocol was designed with smart clients and dumb servers in mind, though I'm sure some of that has changed over time - but that design decision doesn't lend itself as well to clients on battery-constrained devices.
Although with that said, the fact that you aren't required to be in the same set of MUCs on every device helps in battery-constrained devices; for example I only stay joined to the rooms that my friends are in from my phone, unless I need to join another one temporarily.
Although now that I read the spec again, it seems general enough that maybe it could be used to implement behavior like that? I don't think I've seen any servers that do, though.
> groupchat messages must set a subject or have the user’s username or nickname mentioned in the messages (or be encrypted) to count as “important”.
For example, Matrix clients on Android/iOS will stay suspended entirely, then will wake up when you receive a push notification. Desktop clients, on the other hand, will stay running and receive every message, even if they're not messages that you necessarily care about/that would notify.
The protocol could in theory have an in-band way to tell the server "hey, I really only care about notifications now, could you only send me those?" but currently it doesn't. By contrast, most Android/iOS apps can rely on push notifications and suspend completely when they're not in the foreground - meaning they're not receiving anything but what's important enough to notify about.