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Apple admits to secretly giving governments push notification data
(arstechnica.com)
This is a most excellent place for technology news and articles.
I think it means that notifications aren't sent, but it's a good question.
Thinking this through a bit more. It's the server (eg. Signal) that sends the push notifications to Apple/Google. So turning off notifications on your phone presumably means that that Apple/Google doesn't send them to your device. However they are presumably still be going from the server to Apple/Google (because how would Signal know that you've turned notifications off on your phone)?
Based on my understanding, Signal (their servers) won't know and neither will Apple. The local app installed on your phone knows, as that's the client handling what to do with the send/receive requests. I've very little experience with mobile development, though, so I could be very off mark here.