feat: Add presence heartbeat for Matrix online status

- matrix-gateway: POST /internal/matrix/presence/online endpoint
- usePresenceHeartbeat hook with activity tracking
- Auto away after 5 min inactivity
- Offline on page close/visibility change
- Integrated in MatrixChatRoom component

backend/infra/db/client.ts

@@ -0,0 +1,20 @@
+/**
+ * Database Client
+ * MVP: Placeholder for future DB connection
+ * TODO: Replace with actual DB client (PostgreSQL, etc.)
+ */
+
+// MVP: No-op
+export const dbClient = {
+  connect: async () => {
+    // TODO: Implement actual DB connection
+    console.log('[DB] Connected (stub)');
+  },
+  
+  disconnect: async () => {
+    // TODO: Implement actual DB disconnection
+    console.log('[DB] Disconnected (stub)');
+  },
+};
+
+