You can rename the tabs in tmux but not sure if there's a way to do dynamic status (I suspect there is but it's probably non trivial to get it to play nice with the harness)
You can do this. In my current tmux session I have four windows each with a status indicator that shows up when that window is running a claude code session. It is a blue animated braille spinner when it is working, a red dot when it needs attention and a green tick when it is finished with its work.
Claude code exposes a bunch of hooks you can use to have tmux commands execute. This is invaluable if you are multi-tasking and need to see at a glance what needs attention.
Was just about to say this. And the application can also try to rename the terminal window title with the OSC 2 escape sequence. Don't think you need more than that. The bell was the general "Something needs your attention" since forever.
