## Why
Tool router construction rebuilds the deferred-tool BM25 index during
session initialization and before each sampling continuation, even when
the searchable tool metadata is unchanged. Local profiling measured
`append_tool_search_executor` at roughly 113 ms per continuation, making
repeated index construction the largest measured router-building cost.
## What changed
- Add a session-scoped `ToolSearchHandlerCache` so continuations and
user turns can reuse the existing handler.
- Key reuse on the complete ordered `Vec<ToolSearchInfo>`, rebuilding
when searchable text, loadable tool specs, source metadata, or ordering
changes.
- Build handlers outside the cache lock and recheck before publishing
them, avoiding holding the mutex during index construction.
## Verification
- `cache_reuses_identical_search_infos_and_rebuilds_changed_inputs`
covers exact cache reuse and invalidation when the ordered search
metadata changes.
- Local rollout profiling showed the initial router build populating the
cache and unchanged later continuations reusing it:
- uncached: 118 ms median across 14 spans from 3 rollouts
- cached: 4 ms median across 12 spans from 3 rollouts
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