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/core/src/client_common_tests.rs

@@ -197,49 +197,3 @@ fn reserializes_shell_outputs_for_function_and_custom_tool_calls() {
         ]
     );
 }
-
-#[test]
-fn tool_search_output_namespace_serializes_with_deferred_child_tools() {
-    let namespace = tools::ToolSearchOutputTool::Namespace(tools::ResponsesApiNamespace {
-        name: "mcp__codex_apps__calendar".to_string(),
-        description: "Plan events".to_string(),
-        tools: vec![tools::ResponsesApiNamespaceTool::Function(
-            tools::ResponsesApiTool {
-                name: "create_event".to_string(),
-                description: "Create a calendar event.".to_string(),
-                strict: false,
-                defer_loading: Some(true),
-                parameters: crate::tools::spec::JsonSchema::Object {
-                    properties: Default::default(),
-                    required: None,
-                    additional_properties: None,
-                },
-                output_schema: None,
-            },
-        )],
-    });
-
-    let value = serde_json::to_value(namespace).expect("serialize namespace");
-
-    assert_eq!(
-        value,
-        serde_json::json!({
-            "type": "namespace",
-            "name": "mcp__codex_apps__calendar",
-            "description": "Plan events",
-            "tools": [
-                {
-                    "type": "function",
-                    "name": "create_event",
-                    "description": "Create a calendar event.",
-                    "strict": false,
-                    "defer_loading": true,
-                    "parameters": {
-                        "type": "object",
-                        "properties": {}
-                    }
-                }
-            ]
-        })
-    );
-}