Add downstream extension API examples

[caijintaoduolacmeng-star]

Summary

• Add sync and async downstream-SDK examples for the ClientExtension API.
• Demonstrate SDK User-Agent tokens, default headers, sync/async event hooks, and API error mapping.
• Document setup and link the new examples from the top-level README.

Closes #56

Verification

• ruff check examples README.md -> All checks passed
• ruff format --check examples -> 2 files already formatted
• ty check examples/ -> All checks passed
• PYTHONUTF8=1 python -m pytest -q -> 242 passed, 28 deselected, 100% coverage
• sync and async payload/client sanity checks -> passed
• git diff --check -> passed