Copilot CLI incorrectly switches back to previous model after switching to BYOK

### Describe the bug

I ran out of AIC while using claude-sonnet-4.6. After exiting GitHub Copilot and resuming my session using BYOK, the Copilot CLI automatically switched back to claude-sonnet-4.6, despite having supposedly switched to the BYOK configuration.

### Affected version

_No response_

### Steps to reproduce the behavior

1. Run out of AIC while using claude-sonnet-4.6.
2. Exit GitHub Copilot.
3. Resume session using BYOK.
4. Observe that Copilot CLI automatically switches back to claude-sonnet-4.6 or showing this:

```
Model 'glm-5.2:cloud' not found on provider at https://ollama.com/v1 (HTTP 404).
Check that the model is available on your provider.
```

### Expected behavior

The CLI should respect the BYOK configuration and not revert to the previously used model after a session restart.

### Additional context

_No response_

首先重現列出的工作階段重新啟動流程：用完 AIC、退出 Copilot CLI，並使用 BYOK 繼續。追蹤 BYOK 設定和所選模型如何還原，包括 Ollama provider 錯誤。完成條件是：繼續的 BYOK 工作階段會保留其設定的模型，而不是還原為先前的模型。

由索引模型根據 Issue 內容生成。