I would like to be notified if my app crashes so it seems that health checks + slack is the way to go there but I cannot stop wondering about fly status which also shows me if my app is running or not so I am wondering it fly could not just notify me when my app restarts instead of my writing a script check if the app process is still alive.
Fly has nothing built-in for this.
You could try send your logs to an external service like LogDNA with the Fly log shipper. Log services tend to have ways to alert on specific log messages, which may be useful for other things in your app.