- Add Send to background header action to Planning Mode, Subtask Breakdown, and Mission Interview modals using a shared minimize icon pattern
- Show the action only during active AI session states and keep it hidden in initial states
- Implement background behavior to close the live stream connection and modal without canceling the underlying AI session
- Add modal tests that verify button visibility rules and confirm send-to-background does not trigger cancel APIs
- Add shared CSS styling for modal send-to-background controls, including hover and focus-visible states
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