Ideally it would support WebPush which would allow your app to register with any push notification service that supports WebPush.
WebSockets would drain battery and also add a lot of load on the servers to handle all those connections. Implementing specific notification services directly on Lemmy isn’t quite where it belongs. Plus you don’t want all Lemmy admins to have to register to Apple Push and Google’s FCM and potentially others. With WebPush you can have your own server as a relay and then dispatch to expo/APN/FCM as needed.