Feature: Add OpenAIAgent backed by OpenAI Response API (#6418)

## Why are these changes needed?

This PR introduces a new `OpenAIAgent` implementation that uses the
[OpenAI Response
API](https://platform.openai.com/docs/guides/responses-vs-chat-completions)
as its backend. The OpenAI Assistant API will be deprecated in 2026, and
the Response API is its successor. This change ensures our codebase is
future-proof and aligned with OpenAI’s latest platform direction.

### Motivation
- **Deprecation Notice:** The OpenAI Assistant API will be deprecated in
2026.
- **Future-Proofing:** The Response API is the recommended replacement
and offers improved capabilities for stateful, multi-turn, and
tool-augmented conversations.
- **AgentChat Compatibility:** The new agent is designed to conform to
the behavior and expectations of `AssistantAgent` in AgentChat, but is
implemented directly on top of the OpenAI Response API.

### Key Changes
- **New Agent:** Adds `OpenAIAgent`, a stateful agent that interacts
with the OpenAI Response API.
- **Stateful Design:** The agent maintains conversation state, tool
usage, and other metadata as required by the Response API.
- **AssistantAgent Parity:** The new agent matches the interface and
behavior of `AssistantAgent` in AgentChat, ensuring a smooth migration
path.
- **Direct OpenAI Integration:** Uses the official `openai` Python
library for all API interactions.
- **Extensible:** Designed to support future enhancements, such as
advanced tool use, function calling, and multi-modal capabilities.

### Migration Path
- Existing users of the Assistant API should migrate to the new
`OpenAIAgent` to ensure long-term compatibility.
- Documentation and examples will be updated to reflect the new agent
and its usage patterns.
### References
- [OpenAI: Responses vs. Chat
Completions](https://platform.openai.com/docs/guides/responses-vs-chat-completions)
- [OpenAI Deprecation
Notice](https://platform.openai.com/docs/guides/responses-vs-chat-completions#deprecation-timeline)
---

## Related issue number

Closes #6032 

## Checks

- [ ] I've included any doc changes needed for
<https://microsoft.github.io/autogen/>. See
<https://github.com/microsoft/autogen/blob/main/CONTRIBUTING.md> to
build and test documentation locally.
- [X] I've added tests (if relevant) corresponding to the changes
introduced in this PR.
- [X] I've made sure all auto checks have passed.

Co-authored-by: Griffin Bassman <griffinbassman@gmail.com>

Author: jay-thakur

python/packages/autogen-ext/src/autogen_ext/agents/openai/__init__.py

@@ -1,10 +1,11 @@
 try:
+    from ._openai_agent import OpenAIAgent
     from ._openai_assistant_agent import OpenAIAssistantAgent
 except ImportError as e:
     raise ImportError(
-        "Dependencies for OpenAIAssistantAgent not found. "
+        "Dependencies for OpenAI agents not found. "
         'Please install autogen-ext with the "openai" extra: '
         'pip install "autogen-ext[openai]"'
     ) from e
 
-__all__ = ["OpenAIAssistantAgent"]
+__all__ = ["OpenAIAssistantAgent", "OpenAIAgent"]