[FEATURE] Add "silent kill" option for background tasks/agents

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

When killing a background task/agent using the keyboard shortcut (k), the AI is always notified that the task was terminated. This can cause unwanted behavior where the AI tries to
recover, restart, or ask questions about the killed task - cluttering the conversation and changing the AI's focus.

Proposed Solution

Add a second kill option in the task management UI:

• Press k - Kill (current behavior, AI is notified)
• Press s (or shift+k) - Silent Kill (AI is NOT informed)

Alternative Solutions

_No response_

Priority

Medium - Would be very helpful

Feature Category

CLI commands and flags

Use Case Example

1. User launches an Explore agent in background to search the codebase
2. The agent is taking too long or going in the wrong direction
3. User navigates with arrow down → selects the task
4. User presses s for silent kill
5. The task is terminated but the AI continues the conversation unaware, without trying to recover or comment on the interruption

Additional Context

This gives users finer control over:

• Conversation flow and context management
• Preventing AI from fixating on failed/cancelled tasks
• Cleaner session history without interruption-related noise