Several ways to handle this: one with hook events and the other telling Claude Code to notify when it’s done or needs your input by using the PushNotification tool. On desktop you get an OS notification and push notification to Claude Mobile if you have remote control on.
Here’s how setup hooks: youtu.be/L8TNQ_jSD90?is=G-Jj…
If you run CC in cmux you’ll get OS notifications without any additional setup too.