## 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`
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