codex-tools: extract tool spec models (#16047)

## Why

This continues the `codex-tools` migration by moving another passive
tool-definition layer out of `codex-core`.

After `ResponsesApiTool` and the lower-level schema adapters moved into
`codex-tools`, `core/src/client_common.rs` was still owning `ToolSpec`
and the web-search request wire types even though they are serialized
data models rather than runtime orchestration. Keeping those types in
`codex-core` makes the crate boundary look smaller than it really is and
leaves non-runtime tool-shape code coupled to core.

## What changed

- moved `ToolSpec`, `ResponsesApiWebSearchFilters`, and
`ResponsesApiWebSearchUserLocation` into
`codex-rs/tools/src/tool_spec.rs`
- added focused unit tests in `codex-rs/tools/src/tool_spec_tests.rs`
for:
  - `ToolSpec::name()`
  - web-search config conversions
  - `ToolSpec` serialization for `web_search` and `tool_search`
- kept `codex-rs/tools/src/lib.rs` exports-only by re-exporting the new
module from `lib.rs`
- reduced `core/src/client_common.rs` to a compatibility shim that
re-exports the extracted tool-spec types for current core call sites
- updated `core/src/tools/spec_tests.rs` to consume the extracted
web-search types directly from `codex-tools`
- updated `codex-rs/tools/README.md` so the crate contract reflects that
`codex-tools` now owns the passive tool-spec request models in addition
to the lower-level Responses API structs

## Test plan

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

## References

- #15923
- #15928
- #15944
- #15953
- #16031

codex-rs/core/src/tools/spec_tests.rs

@@ -1,4 +1,3 @@
-use crate::client_common::tools::FreeformTool;
 use crate::config::test_config;
 use crate::models_manager::manager::ModelsManager;
 use crate::models_manager::model_info::with_config_overrides;
@@ -12,6 +11,9 @@ use codex_protocol::openai_models::InputModality;
 use codex_protocol::openai_models::ModelInfo;
 use codex_protocol::openai_models::ModelsResponse;
 use codex_tools::AdditionalProperties;
+use codex_tools::FreeformTool;
+use codex_tools::ResponsesApiWebSearchFilters;
+use codex_tools::ResponsesApiWebSearchUserLocation;
 use codex_tools::mcp_tool_to_deferred_responses_api_tool;
 use codex_utils_absolute_path::AbsolutePathBuf;
 use pretty_assertions::assert_eq;
@@ -106,14 +108,7 @@ fn deferred_responses_api_tool_serializes_with_defer_loading() {
 }
 
 fn tool_name(tool: &ToolSpec) -> &str {
-    match tool {
-        ToolSpec::Function(ResponsesApiTool { name, .. }) => name,
-        ToolSpec::ToolSearch { .. } => "tool_search",
-        ToolSpec::LocalShell {} => "local_shell",
-        ToolSpec::ImageGeneration { .. } => "image_generation",
-        ToolSpec::WebSearch { .. } => "web_search",
-        ToolSpec::Freeform(FreeformTool { name, .. }) => name,
-    }
+    tool.name()
 }
 
 // Avoid order-based assertions; compare via set containment instead.
@@ -1205,10 +1200,10 @@ fn web_search_config_is_forwarded_to_tool_spec() {
             external_web_access: Some(true),
             filters: web_search_config
                 .filters
-                .map(crate::client_common::tools::ResponsesApiWebSearchFilters::from),
+                .map(ResponsesApiWebSearchFilters::from),
             user_location: web_search_config
                 .user_location
-                .map(crate::client_common::tools::ResponsesApiWebSearchUserLocation::from),
+                .map(ResponsesApiWebSearchUserLocation::from),
             search_context_size: web_search_config.search_context_size,
             search_content_types: None,
         }