fix: Resolve backend logger permission errors

- Fix logger path to use relative path from backend directory
- Add LOG_DIR environment variable support for custom log paths
- Create logs directory with .gitkeep to ensure it exists
- Add docker-entrypoint.sh to handle runtime permissions
- Optimize Dockerfile to set proper permissions for nodejs user
- Ensure logs directory is writable by the application

🤖 Generated with [Claude Code](https://claude.ai/code)

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

docker/Dockerfile.backend

@@ -17,15 +17,18 @@ RUN npm ci --only=production
 # Copy application files
 COPY . .
 
-# Create logs directory
-RUN mkdir -p logs
-
 # Create non-root user
 RUN addgroup -g 1001 -S nodejs && \
     adduser -S nodejs -u 1001
 
-# Change ownership
-RUN chown -R nodejs:nodejs /app
+# Create logs directory with proper permissions
+RUN mkdir -p logs && \
+    chown -R nodejs:nodejs /app && \
+    chmod 755 logs
+
+# Copy and set permissions for entrypoint
+COPY docker-entrypoint.sh /usr/local/bin/
+RUN chmod +x /usr/local/bin/docker-entrypoint.sh
 
 # Switch to non-root user
 USER nodejs
@@ -34,4 +37,4 @@ USER nodejs
 EXPOSE 3000
 
 # Start the application
-CMD ["node", "src/app.js"]
+ENTRYPOINT ["docker-entrypoint.sh"]