feat: Show background tasks status in sidebar

[dccarbone]

Problem

When using background tasks (background_task, call_omo_agent with run_in_background=true), there's no visibility into which tasks are currently running.

The user has to:

1. Remember the task_ids manually
2. Use background_output to check status one by one
3. Hope they don't forget to cancel tasks before finishing

Proposed Solution

Add a visual indicator in the sidebar showing active background tasks:

• Task count badge on sidebar (e.g., "3 running")
• Expandable list showing:
  • Agent type (explore, librarian, oracle, etc.)
  • Task description (the short description passed to the tool)
  • Duration/elapsed time
  • Quick actions: view output, cancel

Why This Matters

• Resource awareness: Users can see if they're spinning up too many agents
• Better UX: No need to track task_ids mentally
• Easier cleanup: One-click cancel instead of background_cancel(all=true)

Alternatives Considered

• Toast notifications for task start/end (less persistent)
• Status bar indicator (less detailed)

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Feature request from a user who frequently uses parallel background agents for exploration.