docs: add Hy3 API quickstart and runnable examples

[dujunjin]

Summary

• add a repository-level Hy3 API quickstart covering connection settings, curl and Python calls, parameters, reasoning modes, tool calling, rate limits, and troubleshooting
• add six runnable Python examples with companion walkthroughs for chat, streaming, latency comparison, tool calling, reasoning modes, and retry handling
• add shared configuration/parsing helpers, explicit bounded retry behavior, dependency files, and discoverability links from both repository READMEs
• add offline tests for configuration, stream parsing, retry classification, documentation links, file contracts, and secret-shaped content

Validation

• ruff format --check --config examples/api/ruff.toml examples/api
• ruff check --config examples/api/ruff.toml examples/api
• pytest -q examples/api/tests (28 passed)
• git diff --check
• staged secret-pattern scan

A live Hy3 endpoint was not available during local verification, so sample output is explicitly marked illustrative rather than presented as a live capture.

Closes #1