Your phone has to be informed somehow, from the internet, that it has data to present as a notification. The fact that you got a notification at 3:32 and then again at 3:35 is trackable data, pretty much no matter what anyone does with it, encrypted or not. Doubly so if someone has MITM attacked your data stream. They may not know what the notification contains or even what app it was sent to, but the act of transmitting and then receiving this data packet over cell network or internet is a trackable event. And I don't really know what Apple could even do about that beyond attempting to build Internet 2 solely for the purposes of keeping the cops out of it, which is unlikely at best.

Honestly I think developers should just use push notifications to tell the app to directly fetch the notification contents from their server, rather than sending the contents of the notification using push, where it is stored by Apple/Google.

Or do what Element and Syncthing do, which is bypass that entire Google push infrastructure (FCM, formerly GCM?) and connect directly to their own ones instead - at the expense of some additional battery consumption, particularly when there's poor cell service. Due to iOS restrictions on background apps, this probably isn't possible on that platform?

Edit: add clarification

Why not chuck the data when it’s no longer being used, though?

They do. Apple is sending literally trillions of push notifications per year and certainly doesn't want to save them longer than necessary (a useless expense), but the government can also ask that information for a targeted user be retained, going forward from the request, even though it would normally be purged.

Because protecting user privacy is not a priority.