Encapsulate tool search entries in handlers (#22261)

## Why

This builds on the handler-owned spec refactor by moving deferred
tool-search metadata to the same handlers that already own tool specs.
The registry builder no longer needs a separate prebuilt
`tool_search_entries` path; it can collect searchable entries from
deferred handlers directly.

## What changed

- Added `search_info()` to tool handlers and implemented it for MCP and
dynamic handlers.
- Reused handler `spec()` output when constructing tool-search entries,
adapting it into the deferred `LoadableToolSpec` shape expected by
`tool_search`.
- Simplified `build_tool_registry_builder(...)` so `tool_search`
registration is based on deferred handlers with search info.
- Removed the old standalone search-entry builders and now-unused
`codex-tools` discovery helper exports.

## Verification

- `cargo test -p codex-core tools::handlers::tool_search::tests:: --
--nocapture`
- `cargo test -p codex-core tools::spec_plan::tests::search_tool --
--nocapture`
- `cargo test -p codex-core tools::spec::tests:: -- --nocapture`
- `cargo test -p codex-core tools::spec_plan::tests:: -- --nocapture`
- `cargo test -p codex-tools`
- `just fix -p codex-core`
- `just fix -p codex-tools`

codex-rs/tools/src/responses_api.rs

@@ -74,21 +74,6 @@ pub fn dynamic_tool_to_responses_api_tool(
     )?))
 }
 
-pub fn dynamic_tool_to_loadable_tool_spec(
-    tool: &DynamicToolSpec,
-) -> Result<LoadableToolSpec, serde_json::Error> {
-    let output_tool = dynamic_tool_to_responses_api_tool(tool)?;
-    Ok(match tool.namespace.as_ref() {
-        Some(namespace) => LoadableToolSpec::Namespace(ResponsesApiNamespace {
-            name: namespace.clone(),
-            // the user doesn't provide a description for dynamic tools, so we use the default
-            description: default_namespace_description(namespace),
-            tools: vec![ResponsesApiNamespaceTool::Function(output_tool)],
-        }),
-        None => LoadableToolSpec::Function(output_tool),
-    })
-}
-
 pub fn coalesce_loadable_tool_specs(
     specs: impl IntoIterator<Item = LoadableToolSpec>,
 ) -> Vec<LoadableToolSpec> {