Auto model fallback on quota limit shows new model in status line but does not resume — requires full restart

### Describe the bug

When the Copilot premium request quota is exhausted mid-session and the model is set to **Auto** (to automatically fall back to another model when the limit is hit), the CLI detects the switch and updates the bottom-left status line to reflect the new model (e.g., `Auto -> GPT-4o`), but **does not resume** the pending response or allow the session to continue. No further prompts are processed. The only recovery is to fully exit and relaunch the CLI.

### Affected version

GitHub Copilot CLI 1.0.44.

### Steps to reproduce the behavior

1. Open Copilot CLI (`copilot`).
2. Use `/model` to set the model to **Auto** (automatic fallback when quota is reached).
3. Submit prompts until the premium request quota is exhausted.
4. Observe the bottom-left status line — it updates to show the fallback model (e.g., `Auto → GPT-4o`).
5. Attempt to continue the conversation or re-submit the last prompt. It will still tell you you've reached limit.
6. Notice the CLI is stuck, no response is generated and no new prompts are processed.

### Expected behavior

After the model automatically switches to the Auto-selected fallback, the CLI should **seamlessly resume**, either retrying the last request automatically or allowing the user to continue the session without any interruption.

### Additional context

- **Operating system:** Linux
- **CPU architecture:** x86_64
- **Terminal emulator:** GNOME Terminal
- **Shell:** bash
- **Installation method:** curl install script
- **Experimental mode enabled:** no
- **Model at time of quota hit:** Claude Sonnet 4.6 (current default)
- **Fallback model shown in status line:** `Auto → GPT-4o`

**Workaround:** Exiting (`ctrl+d` or `ctrl+c×2`) and relaunching `copilot` starts a new session that uses the Auto-selected fallback model normally.

**Note:** The status line correctly reflects the new model after the switch, suggesting the fallback model selection logic *does* trigger, the bug is in the resumption step after switching.

Không có tệp nguồn hoặc bài kiểm thử nào được nêu. Hãy bắt đầu bằng cách tái hiện vấn đề trong Copilot CLI với `/model` được đặt thành Auto, sau đó theo dõi luồng fallback khi đạt giới hạn quota và cập nhật dòng trạng thái. Được xem là hoàn tất khi phiên tiếp tục sau khi chuyển đổi model và chấp nhận prompt tiếp theo mà không cần khởi động lại.

Do mô hình lập chỉ mục viết ra từ nội dung của issue.