Why not just an SMTP extension. Send notifications via email, which expire after X seconds. No need to reinvent the mail
I like Pushover's protocol design: <https://pushover.net/api/client#websocket>
So now you’ve packaged the problem in a new layer that doesn’t solve anything but creates new problems.
The concept of an open connection waiting for the server to say anything is not novel or special, it just, as we already know, doesn’t really work reliably, you have to do more work to make it reliable.