Your argument has become circular, because the what Signal uses push notifications for isn't security-relevant: the messages are empty and used only as a wakeup.
They still contain information, though. They say when you're talking on Signal. Matched with someone else's messages at about the right frequency to indicate a conversation, they give a pretty decent idea of who you're talking to.
If I say "your house is on fire!" and you rebut "no it isn't" and I respond "well, your shoelace is untied", any reasonable observer will conclude that you've conceded the house fire.
If my house was really on fire, you'd say "no, really, look at it! Flames are shooting out of the bedroom window!". If your strong argument was valid, you'd restate it, perhaps with additional evidence.
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