Background agent completion retention

### Describe the bug

Completed background agents are purged from the CLI agent registry very quickly, so read_agent can
return Agent not found even after a successful completion notification.

Summary
Background agents are retrievable while running, but completed agents appear to have only a very short retention
window. In this session, the original code-review-auditor agent auth-audit showed as running for several minutes,
then later vanished entirely from list_agents, and read_agent returned Agent not found. A separate live repro showed
the same behavior with tiny probe agents, so this does not look specific to the custom reviewer.

### Affected version
GitHub Copilot CLI 1.0.21.

### Steps to reproduce the behavior

1. Start a tiny background agent.
2. Confirm it appears in list_agents while running.
3. Wait for completion notification.
4. Immediately call read_agent / list_agents --include_completed and observe it is briefly available.
5. Wait a few more seconds and call them again.
6. The completed agent disappears from list_agents, and read_agent returns no agent found.

### Expected behavior

Completed background agents should remain readable/listed for a reasonable period, at least long enough for normal
follow-up after the completion notification.

### Additional context

Actual
Completed agents are purged very quickly after finishing, sometimes within a few seconds of post-completion access.

Impact
Long-running background reviews can finish successfully but become unrecoverable before the user or orchestrator
reads the result, which makes background mode unreliable for required audit outputs.

Evidence from this session

- auth-audit was started and later observed as still running.
- Later, read_agent(auth-audit) returned Agent not found.
- Live repro agents showed the same short-lived post-completion availability.

Current workaround

- Use mode: "sync" when the result must be preserved before handoff.
- If using background, read and capture the result immediately after completion.

Start with the background-agent implementation behind the read_agent and list_agents entry points, comparing behavior while agents are running with list_agents --include_completed after completion. Reproduce the short post-completion retention window using a tiny background agent, then verify that completed agents remain readable and listed long enough for normal follow-up.

索引モデルが issue の本文から書いたものです。