The Android application is quite dead for me (but not to me) - I've been messing with an alternate app, but the lack of notifications is still a pain.
The 'long term' alternative would be to get web push notifications as suggested, but that's going to take an indefinite amount of time to be a thing.
In discussing alternatives with the dev of another, unofficial SE client, it was mentioned that
Would love to bring push notifications to the app, but unfortunately part of this implementation requires server-side implementation of Firebase Cloud Messaging. It seems like things are still up and running on the Stack Exchange side, but I'm not sure if the API to register a device for push is public.
It's a bit of a strange thing to ask, and I know lots of the mobile APIs still secret squirrel, but would it be an option to informally (or formally!) open this up, and give some heads-up before the notifications API and backend is sunset?