Copilot Does Not Change Model

### Describe the bug

When attempting to change the AI model in GitHub Copilot Chat within VS Code, the model does not change.

### Affected version

GitHub Copilot CLI 1.0.19

### Steps to reproduce the behavior

1. Open Copilot in VSCode or CLI in terminal
2. use /model command
3. Click the model selector dropdown
4. Select a different model from the list
5. Observe that the model is unchanged

### Expected behavior

The newly selected model should be saved and used for subsequent Copilot Chat responses. The model selector should reflect the
chosen model persistently.

### Additional context

- Current Model: Claude Sonnet 4.6 (medium)
- Editor: Visual Studio Code
- Extension: GitHub Copilot / GitHub Copilot Chat
- The issue occurs each time a model change is attempted; the selection does not stick
- Workstation also has Claude Code, gstack

首先使用列出的版本和步驟，透過 Copilot CLI 中的 /model 命令以及 VS Code 中的模型選擇器重現此問題。追蹤所選模型的儲存位置，以及它如何套用至後續聊天回應。當選取其他模型後該選取能夠持續保存，且選擇器在後續回應中反映該模型時，即表示完成。

由索引模型根據 Issue 內容生成。