My main issue is you're dependent on google centralized cloud service for a good UX of getting notifications when something happens interesting to you.

In the spirit of decentralized freedom tech which I believe nostr is, the natural path for having that nice UX feature should be to do it also in a decentralized, third-party risk free, uncensorable way.

Should not have to be too expensive to keep a socket to a few relays in the device open, or just pull then periodically.

For sure google push services also does this somewhere/somehow for connection with fcm cloud, just lower level taking advantage of privileged access to the system.

That should be a choice for the end user, not a forced dictated imposed thing.