docs(examples): add async streaming examples for Responses and Chat

[lucasalencarxisto-stack]

This PR adds two new async streaming examples under examples/:

• async_responses_stream.py – Demonstrates async streaming with the Responses API, which is now the recommended primary API.

• async_chat_stream.py – Shows async streaming with Chat Completions, still supported indefinitely for users migrating gradually.

Both scripts:

• Use AsyncOpenAI and asyncio.run(...).

• Include a Rye shebang to follow the contributing guide.

• Provide minimal, working async loops that print incremental events/chunks for demo purposes.

These additions improve developer experience by providing clear, runnable async/streaming examples for both the new and legacy APIs without modifying existing examples.

[lucasalencarxisto-stack]

Hi team, thanks for maintaining this project! 🙌
I noticed there wasn’t an async streaming example for the new Responses API, so I added one, along with a matching Chat Completions async streaming example for users still on that API. Hopefully this makes it easier for newcomers to try async/streaming right away. Feedback is very welcome!

[lucasalencarxisto-stack]

Just updated the PR to include the actual file contents (previously empty by mistake). The examples are now complete and ready for review. Thanks for your time! 🙌