[Task] Split examples into separate files under `examples/`

[Apricot-S]

Summary

All example code is currently stored in a single file (doc/examples.py).
This issue proposes moving the examples into a new top‑level examples/ directory and splitting them into multiple files based on use cases.

Motivation

• The current single-file structure makes examples harder to navigate
• Splitting by use case improves readability and discoverability
• A dedicated examples/ directory is a more conventional layout
• Easier to add or update examples

Proposed changes

• Create a new examples/ directory at the project root
• Move doc/examples.py into this directory
• Split the content into multiple files, such as:
  • examples/basic_usage.py
  • examples/hand_evaluation.py
  • examples/yaku_examples.py
  • examples/advanced_features.py
• Update wiki links that reference the old path