[codex] Make handlers own parallel tool support (#22254)

## Why

`ToolRouter::tool_supports_parallel()` was still consulting configured
specs when a handler lookup missed, even though parallel schedulability
is really a property of the executable handler. Keeping that metadata on
`ConfiguredToolSpec` duplicated state between the model-visible spec
layer and the runtime handler layer.

This change makes handlers the sole source of truth for parallel tool
support and removes the extra spec wrapper that only existed to carry
duplicated metadata.

## What changed

- removed `ConfiguredToolSpec` and store plain `ToolSpec` values in the
registry/router builder path
- changed `ToolRouter::tool_supports_parallel()` to consult only the
handler registry and fall back to `false`
- simplified spec collection and test helpers to operate directly on
`ToolSpec`
- updated router/spec tests to cover handler-owned parallel behavior and
the no-handler fallback

## Validation

- `cargo test -p codex-tools`
- `cargo test -p codex-core mcp_parallel_support_uses_handler_data`
- `cargo test -p codex-core
deferred_responses_api_tool_serializes_with_defer_loading`
- `cargo test -p codex-core
tools_without_handlers_do_not_support_parallel`
- `cargo test -p codex-core
request_plugin_install_can_be_registered_without_search_tool`

## Docs

No documentation updates needed.

codex-rs/tools/src/lib.rs

@@ -76,7 +76,6 @@ pub use tool_discovery::collect_request_plugin_install_entries;
 pub use tool_discovery::collect_tool_search_source_infos;
 pub use tool_discovery::filter_request_plugin_install_discoverable_tools_for_client;
 pub use tool_discovery::tool_search_result_source_to_loadable_tool_spec;
-pub use tool_spec::ConfiguredToolSpec;
 pub use tool_spec::ResponsesApiWebSearchFilters;
 pub use tool_spec::ResponsesApiWebSearchUserLocation;
 pub use tool_spec::ToolSpec;

codex-rs/tools/src/tool_spec.rs

@@ -75,25 +75,6 @@ impl From<LoadableToolSpec> for ToolSpec {
     }
 }
 
-#[derive(Debug, Clone, PartialEq)]
-pub struct ConfiguredToolSpec {
-    pub spec: ToolSpec,
-    pub supports_parallel_tool_calls: bool,
-}
-
-impl ConfiguredToolSpec {
-    pub fn new(spec: ToolSpec, supports_parallel_tool_calls: bool) -> Self {
-        Self {
-            spec,
-            supports_parallel_tool_calls,
-        }
-    }
-
-    pub fn name(&self) -> &str {
-        self.spec.name()
-    }
-}
-
 /// Returns JSON values that are compatible with Function Calling in the
 /// Responses API:
 /// https://platform.openai.com/docs/guides/function-calling?api-mode=responses

codex-rs/tools/src/tool_spec_tests.rs

@@ -1,4 +1,3 @@
-use super::ConfiguredToolSpec;
 use super::ResponsesApiNamespace;
 use super::ResponsesApiWebSearchFilters;
 use super::ResponsesApiWebSearchUserLocation;
@@ -92,29 +91,6 @@ fn tool_spec_name_covers_all_variants() {
     );
 }
 
-#[test]
-fn configured_tool_spec_name_delegates_to_tool_spec() {
-    assert_eq!(
-        ConfiguredToolSpec::new(
-            ToolSpec::Function(ResponsesApiTool {
-                name: "lookup_order".to_string(),
-                description: "Look up an order".to_string(),
-                strict: false,
-                defer_loading: None,
-                parameters: JsonSchema::object(
-                    BTreeMap::new(),
-                    /*required*/ None,
-                    /*additional_properties*/ None
-                ),
-                output_schema: None,
-            }),
-            /*supports_parallel_tool_calls*/ true,
-        )
-        .name(),
-        "lookup_order"
-    );
-}
-
 #[test]
 fn web_search_config_converts_to_responses_api_types() {
     assert_eq!(