Sub-agents spawned by background agents appear in UI without user notification

### Describe the bug

When a background general-purpose agent spawns a child agent,
the child appears in the /tasks panel silently — no chat message,
no explanation of why it was started or what it does.

### Affected version

_No response_

### Steps to reproduce the behavior

1. Launch a general-purpose agent in background mode with a complex task
2. The agent internally spawns a sub-agent (e.g. to split work)
3. The sub-agent appears in /tasks panel with a different name/description
4. User has no idea who started it or why

## Actual behavior
Silent appearance in /tasks. User can only discover it via /tasks panel.

### Expected behavior

Any agent launched (directly or by another agent) should post a notification in the chat explaining what it is and who started it.

### Additional context

The parent agent also hung for 18+ minutes (7 tool_calls) with no
timeout or warning, then its child continued working after the parent
was killed.

Use the reproduction steps to trace how background agents and their child agents are registered for the /tasks panel, then identify the existing chat-notification entry point. Done means a child agent's appearance produces a chat notification that explains what it does and identifies its parent, with coverage for the background-agent case.

索引モデルが issue の本文から書いたものです。