I like getting a push notification when someone reacts or replies to me on Cake, but if it also added a badge to the icon then I'd feel like I have to go do something to make the badge disappear, and that feels like a chore.
Interesting, the only push notifications I find useful are the weather alerts I get from my Accuweather app. They are useful to me because they provide specific details of what the severe weather is (tornado watch until 6pm, extreme cold advisory until Tuesday night, etc).
For gmail, I prefer seeing the unread count on my app, i.e. a badge. I used to use the badge notification for Twitter, however, I sometimes contribute to threads that turn into a storm of likes and retweets, which turns the badge count into noise instead of signal.
The push notifications from the Cake app aren’t intrusive. However, it might be nice to know whether it is for a reaction, a mention, or a post—especially if I’m participating in a great discussion like this.
My two cents, for what it’s worth.