Add tests and implement functionality for staged cascade search and LSP expansion

- Introduced a new JSON file for verbose output of the Codex Lens search results.
- Added unit tests for binary search functionality in `test_stage1_binary_search_uses_chunk_lines.py`.
- Implemented regression tests for staged cascade Stage 2 expansion depth in `test_staged_cascade_lsp_depth.py`.
- Created unit tests for staged cascade Stage 2 realtime LSP graph expansion in `test_staged_cascade_realtime_lsp.py`.
- Enhanced the ChainSearchEngine to respect configuration settings for staged LSP depth and improve search accuracy.

codex-lens/src/codexlens/config.py

@@ -145,6 +145,11 @@ class Config:
     # Staged cascade search configuration (4-stage pipeline)
     staged_coarse_k: int = 200  # Number of coarse candidates from Stage 1 binary search
     staged_lsp_depth: int = 2  # LSP relationship expansion depth in Stage 2
+    staged_stage2_mode: str = "precomputed"  # "precomputed" (graph_neighbors) | "realtime" (LSP)
+    staged_realtime_lsp_timeout_s: float = 10.0  # Max time budget for realtime LSP expansion
+    staged_realtime_lsp_max_nodes: int = 100  # Node cap for realtime graph expansion
+    staged_realtime_lsp_warmup_s: float = 2.0  # Wait for server analysis after opening seed docs
+    staged_realtime_lsp_resolve_symbols: bool = False  # If True, resolves symbol names via documentSymbol (slower)
     staged_clustering_strategy: str = "auto"  # "auto", "hdbscan", "dbscan", "frequency", "noop"
     staged_clustering_min_size: int = 3  # Minimum cluster size for Stage 3 grouping
     enable_staged_rerank: bool = True  # Enable optional cross-encoder reranking in Stage 4