E2E Push Notifications?

[qub]

I didn't have much luck finding information about this on my own, so I'm asking here. Do push notifications happen in an E2E way? From what I understand, riot/element uses matrix.org's free push gateway. For my use case, I would be interested in running my own but still sending push through matrix.org if possible since I don't have my own push keys.

I suppose this is also a question that involves the web and iOS clients, so please redirect me to the appropriate project if there's a better forum to ask this. Thank you!