codex-tools: extract responses API tool models (#16031)

## Why

The previous extraction steps moved shared tool-schema parsing into
`codex-tools`, but `codex-core` still owned the generic Responses API
tool models and the last adapter layer that turned parsed tool
definitions into `ResponsesApiTool` values.

That left `core/src/tools/spec.rs` and `core/src/client_common.rs`
holding a chunk of tool-shaping code that does not need session state,
runtime plumbing, or any other `codex-core`-specific dependency. As a
result, `codex-tools` owned the parsed tool definition, but `codex-core`
still owned the generic wire model that those definitions are converted
into.

This change moves that boundary one step further. `codex-tools` now owns
the reusable Responses/tool wire structs and the shared conversion
helpers for dynamic tools, MCP tools, and deferred MCP aliases.
`codex-core` continues to own `ToolSpec` orchestration and the remaining
web-search-specific request shapes.

## What changed

- added `tools/src/responses_api.rs` to own `ResponsesApiTool`,
`FreeformTool`, `ToolSearchOutputTool`, namespace output types, and the
shared `ToolDefinition -> ResponsesApiTool` adapter helpers
- added `tools/src/responses_api_tests.rs` for deferred-loading
behavior, adapter coverage, and namespace serialization coverage
- rewired `core/src/tools/spec.rs` to use the extracted dynamic/MCP
adapter helpers instead of defining those conversions locally
- rewired `core/src/tools/handlers/tool_search.rs` to use the extracted
deferred MCP adapter and namespace output types directly
- slimmed `core/src/client_common.rs` so it now keeps `ToolSpec` and the
web-search-specific wire types, while reusing the extracted tool models
from `codex-tools`
- moved the extracted seam tests out of `core` and updated
`codex-rs/tools/README.md` plus `tools/src/lib.rs` to reflect the
expanded `codex-tools` boundary

## Test plan

- `cargo test -p codex-tools`
- `cargo test -p codex-core --lib tools::spec::`
- `cargo test -p codex-core --lib tools::handlers::tool_search::`
- `just fix -p codex-tools -p codex-core`
- `just argument-comment-lint`

## References

- [#15923](https://github.com/openai/codex/pull/15923) `codex-tools:
extract shared tool schema parsing`
- [#15928](https://github.com/openai/codex/pull/15928) `codex-tools:
extract MCP schema adapters`
- [#15944](https://github.com/openai/codex/pull/15944) `codex-tools:
extract dynamic tool adapters`
- [#15953](https://github.com/openai/codex/pull/15953) `codex-tools:
introduce named tool definitions`

codex-rs/tools/src/lib.rs

@@ -1,8 +1,10 @@
-//! Shared tool-schema parsing primitives that can live outside `codex-core`.
+//! Shared tool definitions and Responses API tool primitives that can live
+//! outside `codex-core`.
 
 mod dynamic_tool;
 mod json_schema;
 mod mcp_tool;
+mod responses_api;
 mod tool_definition;
 
 pub use dynamic_tool::parse_dynamic_tool;
@@ -11,4 +13,14 @@ pub use json_schema::JsonSchema;
 pub use json_schema::parse_tool_input_schema;
 pub use mcp_tool::mcp_call_tool_result_output_schema;
 pub use mcp_tool::parse_mcp_tool;
+pub use responses_api::FreeformTool;
+pub use responses_api::FreeformToolFormat;
+pub use responses_api::ResponsesApiNamespace;
+pub use responses_api::ResponsesApiNamespaceTool;
+pub use responses_api::ResponsesApiTool;
+pub use responses_api::ToolSearchOutputTool;
+pub use responses_api::dynamic_tool_to_responses_api_tool;
+pub use responses_api::mcp_tool_to_deferred_responses_api_tool;
+pub use responses_api::mcp_tool_to_responses_api_tool;
+pub use responses_api::tool_definition_to_responses_api_tool;
 pub use tool_definition::ToolDefinition;