feat(backend): implement all missing endpoints, real analytics queries, and WebSocket server

- Replace stub analytics.repository.ts with real PostgreSQL queries using pg.Pool
- Add /api/guilds, /api/config, /api/auth/login, /api/ui-state (GET/POST)
- Add /api/review, /api/recordings, /api/analysis/search
- Add /api/messages/:id/reanalyze endpoint
- Add /api/analytics/heatmap and /api/analytics/topics
- Implement media routes (stub responses, backend has no Discord voice client)
- Add WebSocket server at /ws with heartbeat and broadcast functions
- Fix analytics route paths to match frontend contract (dual paths for backward compat)
- Export getPool() from database module for raw SQL queries
- Register all new routers in app.ts

Co-Authored-By: Claude Opus 4.8 <noreply@anthropic.com>

services/backend/src/shared/database/index.ts

@@ -48,6 +48,15 @@ export function getDatabase() {
   return db;
 }
 
+export function getPool() {
+  if (!pool) {
+    throw new Error(
+      "Database not initialized. Call initializeDatabase() first.",
+    );
+  }
+  return pool;
+}
+
 export async function closeDatabase() {
   if (pool) {
     await pool.end();