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

Author: Lucas Alencar Xisto

examples/async_chat_stream.py

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+
+#!/usr/bin/env -S rye run python
+import asyncio
+from openai import AsyncOpenAI
+
+client = AsyncOpenAI()
+
+async def main() -> None:
+    # Chat Completions is still supported indefinitely, but it's no longer the primary API.
+    # This example remains useful for users who still rely on chat.completions.
+    stream = await client.chat.completions.create(
+        model="gpt-4o-mini",
+        messages=[{"role": "user", "content": "Say this is a test (streaming)."}],
+        stream=True,
+    )
+    async for chunk in stream:
+        # Some users prefer accessing delta objects; for demo purposes, printing the chunk is enough.
+        print(chunk)
+
+if __name__ == "__main__":
+    asyncio.run(main())
+

examples/async_responses_stream.py

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+
+#!/usr/bin/env -S rye run python
+import asyncio
+from openai import AsyncOpenAI
+
+client = AsyncOpenAI()
+
+async def main() -> None:
+    # Async streaming with the Responses API (the recommended primary API).
+    stream = await client.responses.create(
+        model="gpt-4o-mini",
+        input="Write a one-sentence bedtime story about a unicorn.",
+        stream=True,
+    )
+    async for event in stream:
+        # Each event may contain deltas and final results; printing directly is sufficient for demo purposes.
+        print(event)
+
+if __name__ == "__main__":
+    asyncio.run(main())
+