Any way to subscribe to the notifications into Python or similar?
So I can run my own custom filters before I decide what and when the notification should be delivered. Could also use the notifications to trigger automations.
I don't think there's any way to access iOS notifications outside the device. If the notifications you care about are also available via email you can disable the official app's notifications and use email rules to redirect specific email notifications to something like Pushover, essentially rolling your own push notifications where you can use rules to control what gets through.
This is an outstanding suggestion. Rife for abuse, but no more abuse than anything else.