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_

首先复现列出的会话重启流程：用完 AIC，退出 Copilot CLI，然后使用 BYOK 恢复。跟踪 BYOK 配置和所选模型的恢复过程，包括 Ollama provider 错误。完成标准是：恢复后的 BYOK 会话保留其配置的模型，而不是恢复为之前的模型。

由索引模型根据 Issue 内容生成。