Add mdbook documentation with runnable examples and GitHub Pages deployment

[wyenox]

Documentation

• Created comprehensive mdbook documentation covering:
  • Getting started guide and core concepts
  • Built-in API clients (chat completions, image generation, speech-to-text, realtime)
  • ChatController for building chat applications
  • RouterClient for composing multiple clients
  • Custom client implementation guide (placeholder)

Runnable Examples

• Added three new examples in examples/ as reference implementations:
  • hello-world - Simple chat completion with streaming
  • tool-calls - Full tool calling workflow with mock weather function
  • image-generation - Image generation with file saving