Its hard to achieve in a decentralised way. Its possible to do it on the client side but if you had 2 nostr apps which both had push notifications enabled, you'd be getting duplicates all the time which would be pretty annoying
Discussion
Totally agree on the push notification annoyances. I get them from one client (it's not many so I'll leave it for now). I wish for a little dot to appear on the nostrudel bell when a new message is there. That way, when I go to nostrudel, a glance shows me "you've got mail."