## Description
This PR cuts Codex over from generic `ResponseItem.metadata` (introduced
here: https://github.com/openai/codex/pull/28355) to
`ResponseItem.internal_chat_message_metadata_passthrough`, which is the
blessed path and has strongly-typed keys.
For now we have to drop this MAv2 usage of `metadata`:
https://github.com/openai/codex/pull/28561 until we figure out where
that should live.
## Description
This PR adds an optional `metadata` field to `ResponseItem` for
Responses API calls. Only mechanical plumbing, no actual values
populated and sent yet. Turns out just adding a new field to
`ResponseItem` has quite a large blast radius already.
This change is backwards compatible because `metadata` is optional and
omitted when absent, so existing response items and rollout history
without it still deserialize and requests that do not set it keep the
same wire shape. For provider compatibility, we strip out `metadata`
before non-OpenAI Responses requests so Azure and AWS Bedrock never see
this field.
My followup PR here will actually make use of it to start storing and
passing along `turn_id`: https://github.com/openai/codex/pull/28360
## What changed
- Added `ResponseItemMetadata` with optional `turn_id`, plus optional
`metadata` on Responses API item variants and inter-agent communication.
- Preserved item metadata through response-item rewrites such as
truncation, missing tool-output synthesis, compaction history
rebuilding, visible-history conversion, rollout/resume, and generated
app-server schemas/types.
- Strip item metadata from non-OpenAI Responses requests while
preserving it for OpenAI-shaped requests.
- Updated the mechanical fixture/test construction churn required by the
new optional field.
## Summary
Add the extension-backed standalone `web.run` tool so Codex can call the
standalone search endpoint through the `codex-api` search client and
return its encrypted output to Responses.
- gate the new tool behind `standalone_web_search`
- install the extension in the app-server thread registry and hide
hosted `web_search` when standalone search is enabled for OpenAI
providers so the two paths stay mutually exclusive
- build search context from persisted history using a small tail
heuristic: previous user message, assistant text between the last two
user turns capped at about 1k tokens, and current user message
## Test Plan
- `cargo test -p codex-web-search-extension`
- `cargo test -p codex-api`
- `cargo test -p codex-core
hosted_tools_follow_provider_auth_model_and_config_gates`
Owen Lin