fix: Replace socket.io with native WS adapter — fixes WebSocket 1006

Frontend uses native WebSocket API, backend was using socket.io which
speaks an incompatible protocol. Switched to @nestjs/platform-ws so
both sides speak native WebSocket. Also fixed JWT TTL override in
docker-compose.yml (was hardcoded to 900s, now 14400s/4h).

Co-Authored-By: Claude Opus 4.6 <noreply@anthropic.com>

backend-nest/package.json

@@ -20,7 +20,7 @@
     "@nestjs/microservices": "^10.4.0",
     "@nestjs/passport": "^10.0.3",
     "@nestjs/platform-express": "^10.4.0",
-    "@nestjs/platform-socket.io": "^10.4.0",
+    "@nestjs/platform-ws": "^10.4.22",
     "@nestjs/schedule": "^4.0.0",
     "@nestjs/swagger": "^7.3.0",
     "@nestjs/typeorm": "^10.0.2",
@@ -38,7 +38,8 @@
     "rxjs": "^7.8.1",
     "swagger-ui-express": "^5.0.0",
     "typeorm": "^0.3.20",
-    "uuid": "^9.0.0"
+    "uuid": "^9.0.0",
+    "ws": "^8.19.0"
   },
   "devDependencies": {
     "@nestjs/cli": "^10.4.0",
@@ -49,6 +50,7 @@
     "@types/passport-jwt": "^4.0.1",
     "@types/qrcode": "^1.5.5",
     "@types/uuid": "^9.0.8",
+    "@types/ws": "^8.18.1",
     "typescript": "^5.4.0"
   }
 }