AssistantMessageDeltaEvent and AssistantReasoningEvent not triggered due to unhandled reasoning field from BYOK providers (Copilot CLI)

### Describe the bug

When using GitHub Copilot CLI (or SDK) with BYOK and vLLM as the provider, neither AssistantMessageDeltaEvent nor AssistantReasoningEvent are triggered if the reasoning content is returned in the reasoning field. Copilot CLI only checks reasoning_content, so no event is fired or reasoning received. This issue appears with vLLM (and may affect others), and was discovered after inspecting API network responses as detailed in my earlier SDK repo issues. CLI version 1.0.43. SDK version 0.3.0.

### Affected version

1.0.43

### Steps to reproduce the behavior

1. Set BYOK with vLLM as the provider in GitHub Copilot CLI/SDK (Windows or WSL).
2. Trigger completions or events that would yield reasoning.
3. Notice that no AssistantMessageDeltaEvent nor AssistantReasoningEvent is triggered if the response uses the reasoning field instead of reasoning_content.

### Expected behavior

Copilot CLI (and SDK) should process the reasoning field from BYOK providers, not only reasoning_content, so that both events are properly triggered and content received.

### Additional context

- Environment: Windows, WSL
- Copilot CLI version: 1.0.43
- Copilot SDK version: 0.3.0
- BYOK Provider: vLLM

GitHub Copilot CLI または SDK 0.3.0、BYOK、vLLM を使用して問題を再現し、その後 reasoning_content を読み取るイベント処理を調査してください。レポートで説明されているレスポンスフィールドを比較し、AssistantMessageDeltaEvent と AssistantReasoningEvent がコンテンツを受け取るように reasoning が処理されていることを確認してください。

索引モデルが issue の本文から書いたものです。