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/ws/broadcast.ts

@@ -0,0 +1,35 @@
+/**
+ * Global broadcast functions for WebSocket events.
+ *
+ * These are assigned by ws/server.ts when the WebSocket server initializes.
+ * Other modules call them to push real-time events to connected frontend clients.
+ *
+ * Usage:
+ *   import { broadcastMessageCreated } from "../ws/broadcast.js";
+ *   broadcastMessageCreated(messageData);
+ */
+
+type BroadcastFn = (data: unknown) => void;
+
+// Extend globalThis with broadcast function types
+declare global {
+  // biome-ignore lint/suspicious/noAssignInExpressions: intentional global broadcast registry
+  var broadcastMessageCreated: BroadcastFn | undefined;
+  var broadcastMessageUpdated: BroadcastFn | undefined;
+  var broadcastMessageDeleted: BroadcastFn | undefined;
+  var broadcastAttachmentUploaded: BroadcastFn | undefined;
+}
+
+const noop: BroadcastFn = () => {};
+
+export const broadcastMessageCreated: BroadcastFn = (...args) =>
+  (globalThis.broadcastMessageCreated ?? noop)(...args);
+
+export const broadcastMessageUpdated: BroadcastFn = (...args) =>
+  (globalThis.broadcastMessageUpdated ?? noop)(...args);
+
+export const broadcastMessageDeleted: BroadcastFn = (...args) =>
+  (globalThis.broadcastMessageDeleted ?? noop)(...args);
+
+export const broadcastAttachmentUploaded: BroadcastFn = (...args) =>
+  (globalThis.broadcastAttachmentUploaded ?? noop)(...args);