## What changed
- Add optional serialized Codex turn metadata to extension tool calls.
- Populate it from the current turn context and send it as the
`x-codex-turn-metadata` header on standalone web search requests.
## Testing
- Extend the app-server web search integration test to verify that client
metadata, including the model ID, reaches the standalone search request.
GitOrigin-RevId: c0950108d89a1d317ac94ccd23efcee72fffc6f0