[FEATURE] Hide cursor in inactive tmux panes

Preflight Checklist

• [x] I have searched existing requests and this feature hasn't been requested yet
• [x] This is a single feature request (not multiple features)

Problem Statement

If you're running claude in multiple tmux panes, the cursor remains active in each of them. So if you look away from the screen for a while then look back at it, there's no easy way of knowing which pane will receive the next key press.

Here's a screenshot from tmux in iTerm 2 with three claude sessions open - note that they all show active cursors:

<img width="2292" height="2118" alt="Image" src="https://github.com/user-attachments/assets/d3ddae4e-1770-492f-a0ac-247e8edf79c9" />

Proposed Solution

Other apps such vim and the shell hide the cursor when their pane isn't active. I think it would be really useful if claude did the same.

Alternative Solutions

I currently work around this by guessing which pane will receive the key press and often getting it wrong, in which case I need to delete what I entered and move to the correct pane. If only the active pane showed a cursor, I'd avoid this little routine many times a day.

Priority

Medium - Would be very helpful

Feature Category

CLI commands and flags

Use Case Example

_No response_

Additional Context

_No response_