UI shows background agents as 'running' after they have completed

## Description

The terminal UI displays background agents/tasks as still running (e.g., "10 background tasks running") even after all agents have completed and their results have been successfully retrieved via `read_agent`.

## Steps to Reproduce

1. Launch multiple background agents (e.g., 9 bitsmith agents in parallel)
2. Wait for all agents to complete (receive completion notifications)
3. Retrieve results from each with `read_agent`
4. Observe the UI still shows tasks as "running"

## Expected Behavior

Once an agent completes and its results are read, it should no longer appear as a running task in the UI.

## Actual Behavior

The UI continues to show completed agents as running. `list_agents` correctly returns no running agents, but the UI indicator doesn't update.

## Environment

- Copilot CLI version: 1.0.49
- OS: macOS (Darwin)
- Model: Claude Opus 4.6

從終端 UI 的背景工作指示器開始，追蹤進入點 `read_agent` 取得結果後其狀態如何更新。當所有 agent 都已完成時，將該狀態與 `list_agents` 的空結果進行比較。完成的標準是：讀取結果後，UI 不再將已完成的 agent 計為正在執行。

由索引模型根據 Issue 內容生成。