Track translated Responses hosted/deferred tool semantics

Context

Codex sends OpenAI Responses tool entries such as tool_search and namespace for client-executed deferred tool discovery. That path is used to discover tools that are not eagerly sent in the initial request, including built-in subagent tools. Native Responses targets need to see those entries unchanged so the model can emit tool_search_call, the client can execute it locally, and the follow-up tool_search_output can expose the deferred tool definitions.

The gateway source cleanup should only remove upstream-incompatible image_generation entries. This issue tracks the remaining non-native target behavior when the planner translates a Responses request to Messages or Chat Completions.

Current behavior

• packages/translate/src/responses-via-messages/request.ts narrows tools to Responses function and Freeform custom entries. Hosted/deferred entries such as web_search, tool_search, namespace, and image_generation are skipped.
• packages/translate/src/responses-via-chat-completions/request.ts does the same narrowing for Chat Completions.
• Forced hosted/deferred tool_choice values have no target equivalent today and translate to undefined on Messages/Chat paths.

This is acceptable as a documented gap only if the planner/source boundary prevents silent loss for requests that require those tools. It is not a faithful bridge for Codex tool_search/namespace semantics.

Risk

If a Codex Responses request containing tool_search or namespace is routed through a translated target, the selected upstream model will not see the discovery tools and cannot emit tool_search_call. That breaks deferred tool discovery and can make built-in subagent tools unavailable even though the native Responses path would work.

References

• OpenAI Codex ToolSpec::ToolSearch / Namespace: https://github.com/openai/codex/blob/9f42c89c0112771dc29100a6f3fc904049b2655f/codex-rs/tools/src/tool_spec.rs#L17-L27
• OpenAI Codex router handles client-executed ToolSearchCall: https://github.com/openai/codex/blob/9f42c89c0112771dc29100a6f3fc904049b2655f/codex-rs/core/src/tools/router.rs#L106-L123
• OpenAI Codex tool search output shape: https://github.com/openai/codex/blob/9f42c89c0112771dc29100a6f3fc904049b2655f/codex-rs/core/src/tools/context.rs#L166-L180
• OpenAI Codex tests for default tool_search and multi-agent namespace discovery: https://github.com/openai/codex/blob/9f42c89c0112771dc29100a6f3fc904049b2655f/codex-rs/core/tests/suite/search_tool.rs#L116-L158 and https://github.com/openai/codex/blob/9f42c89c0112771dc29100a6f3fc904049b2655f/codex-rs/core/tests/suite/search_tool.rs#L680-L768
• caozhiyuan/copilot-api keeps tool_search / namespace and only strips image_generation by default: https://github.com/caozhiyuan/copilot-api/blob/5d37d5b1ac6566c935a5c26d046396ee5fa423cc/src/routes/responses/handler.ts#L187-L204
• Related OpenAI Codex issue around non-native tool_search handling: https://github.com/openai/codex/issues/20574

Acceptance criteria

• Native Responses requests preserve web_search, tool_search, and namespace tool entries and matching forced tool_choice values.
• Responses-to-Messages and Responses-to-Chat behavior for hosted/deferred tools is explicit: either bridge the supported subset, reject requests that require unbridgeable semantics, or document intentional lossy behavior at the source/planner boundary.
• Tests cover translated tools and forced tool_choice behavior for web_search, tool_search, and namespace.
• TRANSLATION.md states the final policy clearly.

Start with packages/translate/src/responses-via-messages/request.ts and packages/translate/src/responses-via-chat-completions/request.ts, then inspect the existing translation tests and TRANSLATION.md. Trace how Responses tools and forced tool_choice values are handled for native and translated targets. Done means the supported policy is explicit, relevant tool and choice cases are covered by tests, and TRANSLATION.md documents the remaining behavior.