Propagate turn metadata to standalone web search

[XMLIU-oai]

Summary

• attach per-turn Responses API metadata to extension tool calls
• forward that metadata as x-codex-turn-metadata on standalone web search requests
• cover the turn/start to Alpha Search HTTP boundary with an end-to-end regression test

Impact

Currently x-codex-turn-metadata is not passed to standalone web search, which is a metadata-propagation regression.

The header contains Search context, including search_user_metadata, and telemetry attributes such as model_id. Search uses plan, residency, and compliance context when applying provider policy.

Testing

• just test -p codex-app-server standalone_web_search_round_trips_output
• just clippy -p codex-tools -p codex-core -p codex-web-search-extension -p codex-app-server
• just fmt
• git diff --check
• Local Tilt end-to-end validation:
  • started codex-backend and Responses API locally
  • sent an authenticated POST /api/codex/alpha/search request with originator: codex_flora
  • captured the downstream POST /v1/alpha/search request and verified it included x-codex-turn-metadata
  • verified mcp_request_meta -> openai/search_context -> telemetry_attributes.model_id contained the unique test marker
  • ran the production Responses API _model_id_from_headers(...) parser against the captured header and verified it returned the same model ID
  • received HTTP 200 with non-empty encrypted output
  • local Sonic schema DNS was unavailable, so final Sonic metric emission was not validated locally

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[XMLIU-oai]

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