perf(coding-agent): cache grouped search results for skip pagination

[wolfiesch]

What

Add a short-lived, bounded, per-session cache for grouped search results so paginated skip pages reuse the first page's grouped filesystem matches instead of rerunning native grep for each page. Output semantics are unchanged.

• New SearchResultCache (LRU + TTL: 45s, max 8 entries) owned per ToolSession.
• SearchTool.execute looks up the cache only for skip > 0; skip = 0 recomputes and refreshes the entry. The cache key encodes the query, scope, options, and missing-path set.
• Cache is bypassed for line-range selectors, archive members, and internal-URL inputs.
• Successful filesystem mutations clear the per-session cache via invalidateFsScanAfter{Write,Delete,Rename} (now passed the session); handler-owned internal-URL writes call clearSearchResultCache directly.

Why

Paginating a large plain-filesystem search reran the same expensive native grep + grouping for every page. Later pages now reuse the grouped result until the query changes, the TTL expires, or the session mutates files — avoiding repeated work while preserving correctness.

Testing

• bun --cwd=packages/coding-agent test test/tools/search-pagination-cache.test.ts test/tools/search-internal-urls.test.ts test/tools/search-path-lists.test.ts test/tools/multi-search-path.test.ts test/tools/multi-path-missing.test.ts test/tools/search-invalid-regex.test.ts → 70 pass, 0 fail
• bun --cwd=packages/coding-agent run check → biome + tsgo pass
• TDD: new cache tests were written first and confirmed to fail (extra grep calls) before the cache was implemented.

---

• bun check passes
• Tested locally
• CHANGELOG updated (if user-facing)