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/modules/auth/auth.routes.ts

@@ -0,0 +1,32 @@
+import type { Request, Response, Router } from "express";
+import express from "express";
+import { config } from "../../shared/config/index.js";
+import { UnauthorizedError } from "../../shared/errors/index.js";
+import { createChildLogger } from "../../shared/logger/index.js";
+import { asyncHandler } from "../../shared/middlewares/index.js";
+
+const logger = createChildLogger("auth.routes");
+
+const adminPassword = config.ADMIN_PASSWORD || "admin";
+
+export function createAuthRouter(): Router {
+  const router = express.Router();
+
+  // POST /api/auth/login
+  router.post(
+    "/auth/login",
+    asyncHandler(async (req: Request, res: Response) => {
+      const { password } = req.body as { password?: string };
+
+      logger.debug("Auth login attempt");
+
+      if (!password || password !== adminPassword) {
+        throw new UnauthorizedError("Invalid password");
+      }
+
+      res.json({ ok: true });
+    }),
+  );
+
+  return router;
+}