[FEATURE] Kitty mode for teammateMode

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

As a user of the kitty terminal I would really like it the teammateMode supported kitty in addition to tmux and iTerm2

Proposed Solution

Use kitty's control protocol to create split screens similar to the the tmux mode in team mode.

Alternative Solutions

_No response_

Priority

Nice to have

Feature Category

CLI commands and flags

Use Case Example

_No response_

Additional Context

_No response_