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

Reproduce the issue with GitHub Copilot CLI or SDK 0.3.0, BYOK, and vLLM, then inspect the event handling that reads reasoning_content. Compare the response fields described in the report and verify that reasoning is processed so AssistantMessageDeltaEvent and AssistantReasoningEvent receive the content.

Written by the indexing model from the issue text.