Add Docker support with comprehensive deployment options

- Add multi-stage Dockerfile with optimized builds for Go backend and Node.js frontend
- Create docker-entrypoint.sh script for managing both services with PM2
- Add .dockerignore for optimal build context
- Update README.md with Docker deployment documentation including:
  - Docker build and run instructions
  - Persistent data configuration with volume mounts
  - Complete environment variable reference table
  - Docker Compose example configuration

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

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

.dockerignore

@@ -0,0 +1,83 @@
+# Docker ignore file for Claude Code Proxy
+# Excludes unnecessary files from Docker build context
+
+# Git
+.git
+.gitignore
+.gitattributes
+
+# Docker
+Dockerfile
+.dockerignore
+docker-compose*.yml
+
+# Documentation
+README.md
+*.md
+demo.gif
+
+# Environment and config
+.env
+.env.local
+.env.example
+
+# Build artifacts
+bin/
+build/
+dist/
+target/
+
+# Dependencies
+node_modules/
+vendor/
+
+# Cache and temporary files
+.cache/
+.temp/
+.tmp/
+*.tmp
+*.log
+
+# IDE and editor files
+.vscode/
+.idea/
+*.swp
+*.swo
+*~
+
+# OS generated files
+.DS_Store
+.DS_Store?
+._*
+.Spotlight-V100
+.Trashes
+ehthumbs.db
+Thumbs.db
+
+# Database files (will be created in container)
+*.db
+*.sqlite
+*.sqlite3
+requests/
+
+# Web specific
+web/.cache/
+web/build/
+web/dist/
+web/node_modules/
+web/npm-debug.log*
+web/yarn-debug.log*
+web/yarn-error.log*
+
+# Go specific
+proxy/vendor/
+*.test
+*.prof
+coverage.txt
+
+# Logs
+logs/
+*.log
+npm-debug.log*
+yarn-debug.log*
+yarn-error.log*