feat: add production Docker setup with multi-stage builds

- Add production Dockerfiles for frontend and backend
  * Frontend: multi-stage build with nginx serving static files
  * Backend: multi-stage build with Prisma generation
- Create production nginx configuration (nginx/conf.d.prod/)
  * Routes to frontend-prod:80 and backend-prod:3000
  * Supports WebSocket connections for Socket.IO
- Update docker-compose.yml to use production config
  * Add env_file support for backend-prod
  * Mount production nginx config directory
- Add .env.production.example template for deployment

nginx/conf.d.prod/default.conf

@@ -0,0 +1,64 @@
+upstream frontend {
+    server frontend-prod:80;
+}
+
+upstream backend {
+    server backend-prod:3000;
+}
+
+server {
+    listen 80;
+    server_name localhost;
+
+    client_max_body_size 500M;
+
+    # Frontend - Static files served by nginx
+    location / {
+        proxy_pass http://frontend;
+        proxy_http_version 1.1;
+
+        # Standard proxy headers
+        proxy_set_header Host $host;
+        proxy_set_header X-Real-IP $remote_addr;
+        proxy_set_header X-Forwarded-For $proxy_add_x_forwarded_for;
+        proxy_set_header X-Forwarded-Proto $scheme;
+
+        # Timeouts
+        proxy_connect_timeout 60s;
+        proxy_send_timeout 60s;
+        proxy_read_timeout 60s;
+    }
+
+    # Backend API
+    location /api {
+        proxy_pass http://backend;
+        proxy_http_version 1.1;
+
+        proxy_set_header Host $host;
+        proxy_set_header X-Real-IP $remote_addr;
+        proxy_set_header X-Forwarded-For $proxy_add_x_forwarded_for;
+        proxy_set_header X-Forwarded-Proto $scheme;
+
+        # Timeouts
+        proxy_connect_timeout 60s;
+        proxy_send_timeout 60s;
+        proxy_read_timeout 60s;
+    }
+
+    # WebSocket for Socket.IO
+    location /socket.io {
+        proxy_pass http://backend;
+        proxy_http_version 1.1;
+
+        proxy_set_header Upgrade $http_upgrade;
+        proxy_set_header Connection "upgrade";
+        proxy_set_header Host $host;
+        proxy_set_header X-Real-IP $remote_addr;
+        proxy_set_header X-Forwarded-For $proxy_add_x_forwarded_for;
+
+        # Timeouts for WebSocket
+        proxy_connect_timeout 7d;
+        proxy_send_timeout 7d;
+        proxy_read_timeout 7d;
+    }
+}