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

backend/Dockerfile.prod

@@ -0,0 +1,57 @@
+# Multi-stage build for production
+
+# Stage 1: Build
+FROM node:20-alpine AS builder
+
+# Install OpenSSL for Prisma
+RUN apk add --no-cache openssl
+
+WORKDIR /app
+
+# Copy package files
+COPY package*.json ./
+
+# Install all dependencies (including devDependencies for Prisma generation)
+RUN npm ci
+
+# Copy application files
+COPY . .
+
+# Generate Prisma Client
+RUN npx prisma generate
+
+# Stage 2: Production
+FROM node:20-alpine
+
+# Install OpenSSL for Prisma
+RUN apk add --no-cache openssl
+
+WORKDIR /app
+
+# Copy package files
+COPY package*.json ./
+
+# Install only production dependencies
+RUN npm ci --only=production
+
+# Copy application files and generated Prisma Client from builder
+COPY --from=builder /app/src ./src
+COPY --from=builder /app/prisma ./prisma
+COPY --from=builder /app/node_modules/.prisma ./node_modules/.prisma
+COPY --from=builder /app/node_modules/@prisma ./node_modules/@prisma
+
+# Copy entrypoint script
+COPY docker-entrypoint.sh /usr/local/bin/
+RUN chmod +x /usr/local/bin/docker-entrypoint.sh
+
+# Set environment to production
+ENV NODE_ENV=production
+
+# Expose port
+EXPOSE 3000
+
+# Set entrypoint
+ENTRYPOINT ["docker-entrypoint.sh"]
+
+# Start the application
+CMD ["node", "src/server.js"]