Gleason is solid with PWA notifications (they have a central relay). Try adding either 
or else 
and to the home screen and when done sign in. At some stage you should get a prompt to allow notifications as attached. Once you approve then the PWA will show as notification enabled in your notification settings, double check. Then wait for some nostr notifications (replies, reactions) and see if you're getting them even when the app isn't active.
Ditto
Ditto
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Gleasonator
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