Add benchmark results for fast3 and fast4, implement KeepAliveLspBridge, and add tests for staged strategies

- Added new benchmark result files: compare_2026-02-09_score_fast3.json and compare_2026-02-09_score_fast4.json.
- Implemented KeepAliveLspBridge to maintain a persistent LSP connection across multiple queries, improving performance.
- Created unit tests for staged clustering strategies in test_staged_stage3_fast_strategies.py, ensuring correct behavior of score and dir_rr strategies.

codex-lens/tests/test_staged_stage3_fast_strategies.py

@@ -0,0 +1,56 @@
+from __future__ import annotations
+
+from unittest.mock import MagicMock
+
+import pytest
+
+from codexlens.config import Config
+from codexlens.entities import SearchResult
+from codexlens.search.chain_search import ChainSearchEngine
+
+
+def _engine_with_strategy(name: str) -> ChainSearchEngine:
+    cfg = Config.load()
+    cfg.staged_clustering_strategy = name
+    return ChainSearchEngine(registry=MagicMock(), mapper=MagicMock(), config=cfg)
+
+
+def test_stage3_strategy_score_skips_embedding(monkeypatch: pytest.MonkeyPatch) -> None:
+    monkeypatch.setattr(
+        "codexlens.semantic.factory.get_embedder",
+        lambda *a, **k: (_ for _ in ()).throw(RuntimeError("should not embed")),
+    )
+
+    engine = _engine_with_strategy("score")
+    expanded = [
+        SearchResult(path="D:/p/a.py", score=0.9),
+        SearchResult(path="D:/p/a.py", score=0.1),
+        SearchResult(path="D:/p/b.py", score=0.8),
+        SearchResult(path="D:/p/c.py", score=0.7),
+    ]
+
+    reps = engine._stage3_cluster_prune(expanded, target_count=3)
+    assert [r.path for r in reps] == ["D:/p/a.py", "D:/p/b.py", "D:/p/c.py"]
+
+
+def test_stage3_strategy_dir_rr_round_robins_dirs(monkeypatch: pytest.MonkeyPatch) -> None:
+    monkeypatch.setattr(
+        "codexlens.semantic.factory.get_embedder",
+        lambda *a, **k: (_ for _ in ()).throw(RuntimeError("should not embed")),
+    )
+
+    engine = _engine_with_strategy("dir_rr")
+    expanded = [
+        SearchResult(path="D:/p1/a.py", score=0.99),
+        SearchResult(path="D:/p1/b.py", score=0.98),
+        SearchResult(path="D:/p2/c.py", score=0.97),
+        SearchResult(path="D:/p2/d.py", score=0.96),
+        SearchResult(path="D:/p3/e.py", score=0.95),
+    ]
+
+    reps = engine._stage3_cluster_prune(expanded, target_count=4)
+    assert len(reps) == 4
+    assert reps[0].path.endswith("p1/a.py")
+    assert reps[1].path.endswith("p2/c.py")
+    assert reps[2].path.endswith("p3/e.py")
+