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.

ccw/src/core/server.ts

@@ -8,6 +8,7 @@ import { resolvePath, getRecentPaths, normalizePathForDisplay } from '../utils/p
 import { handleStatusRoutes } from './routes/status-routes.js';
 import { handleCliRoutes, cleanupStaleExecutions } from './routes/cli-routes.js';
 import { handleCliSettingsRoutes } from './routes/cli-settings-routes.js';
+import { handleCliSessionsRoutes } from './routes/cli-sessions-routes.js';
 import { handleProviderRoutes } from './routes/provider-routes.js';
 import { handleMemoryRoutes } from './routes/memory-routes.js';
 import { handleCoreMemoryRoutes } from './routes/core-memory-routes.js';
@@ -591,6 +592,11 @@ export async function startServer(options: ServerOptions = {}): Promise<http.Ser
         if (await handleDashboardRoutes(routeContext)) return;
       }
 
+      // CLI sessions (PTY) routes (/api/cli-sessions/*) - independent from /api/cli/*
+      if (pathname.startsWith('/api/cli-sessions')) {
+        if (await handleCliSessionsRoutes(routeContext)) return;
+      }
+
       // CLI routes (/api/cli/*)
       if (pathname.startsWith('/api/cli/')) {
         // CLI Settings routes first (more specific path /api/cli/settings/*)