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/http/server.ts

@@ -1,20 +1,27 @@
+import { createServer, type Server } from "node:http";
 import { config } from "../shared/config/index.js";
 import { initializeDatabase } from "../shared/database/index.js";
 import { createChildLogger } from "../shared/logger/index.js";
 import { createHttpApp } from "./app.js";
+import { createWebSocketServer } from "../ws/server.js";
 
 const logger = createChildLogger("http.server");
 
-export async function startHttpServer() {
+export async function startHttpServer(): Promise<Server> {
   await initializeDatabase();
 
   const app = createHttpApp();
   const port = config.WEBSERVER_PORT;
 
-  return new Promise<void>((resolve, reject) => {
-    const server = app.listen(port, () => {
+  const server = createServer(app);
+
+  // Attach WebSocket server to the same HTTP server
+  createWebSocketServer(server);
+
+  return new Promise<Server>((resolve, reject) => {
+    server.listen(port, () => {
       logger.info({ port }, "HTTP server started");
-      resolve();
+      resolve(server);
     });
 
     server.on("error", (err) => {