Add five production-ready example applications to the repository, demonstrating
advanced SDK integration patterns and real-world use cases.

- phoenix_chat: Real-time chat with Phoenix LiveView, demonstrating WebSocket
  streaming, GenServer session management, and tool usage visualization.
- document_generation: AI-powered Excel creation using elixlsx, showcasing
  natural language parsing, formula generation, and complex styling.
- research_agent: Multi-agent coordination system featuring specialized
  subagents, hook-based lifecycle tracking, and parallel task execution.
- email_agent: Intelligent email assistant with IMAP integration, SQLite
  persistence, and natural language query processing.
- skill_invocation: Demonstration of the Skill tool, including custom
  hook callbacks for tracking invocations and skill execution statistics.