I have a hook in my claude.json that fires on "Stop", it calls a shell script (written by Claude, of course) that calls the Pushover API: https://pushover.net/, which lets you send push notifications to your device. It's paid, but just a one-time fee when you install the app on your phone.

The shell script takes a message which includes Claude's message, but unfortunately there's no deeplinking back to my ssh app (for obvious reasons, the notification just routes you to the pushover app), so instead of tapping the message, I know to just open my Blink shell app to respond to Claude.

This is also quite noisy when I'm just sitting at my desk working, but I usually turn off phone notifications while working anyway.