## Summary
- Normalize deferred MCP and dynamic tools into `ToolSearchEntry` values
before constructing `ToolSearchHandler`.
- Move the tool-search entry adapter out of `tools/handlers` and into
`tools/tool_search_entry.rs` so the handlers directory stays focused on
handlers.
- Keep `ToolSearchHandler` operating over one generic entry list for
BM25 search, namespace grouping, and per-bucket default limits.
## Why
Follow-up cleanup for #17849. The dynamic tool-search support made the
handler juggle source-specific MCP and dynamic tool lists, index
arithmetic, output conversion, and namespace emission. This keeps source
adaptation outside the handler so the search loop itself is smaller and
source-agnostic.
## Validation
- `just fmt`
- `cargo test -p codex-core tools::handlers::tool_search::tests`
- `git diff --check`
- `cargo test -p codex-core` currently fails in unrelated
`plugins::manager::tests::list_marketplaces_ignores_installed_roots_missing_from_config`;
rerunning that single test fails the same way at
`core/src/plugins/manager_tests.rs:1692`.
---------
Co-authored-by: pash <pash@openai.com>
