[Clients]: Add support for OpenAI's Responses API

[marklysze]

Is your feature request related to a problem? Please describe.

OpenAI has released their responses API.

Feature	Chat Completions API	Responses API
Input Format	Messages array with roles (user, assistant, system)	Input parameter accepting multiple text, images, files
Conversation State	Manual management by sending previous messages	Built-in state management with previous_response_id
Tools & Functions	Uses older functions parameter (deprecated)	Support with built-in tools (Web Search/File Search/Computer Use)
Output Structure	Returns message with content	Returns structured output with additional metadata
Store for later retrieval	Need to set store: true	Stores responses by default
Reasoning Models	Less explicit support	New reasoning parameter with effort
Truncation	No explicit strategy parameter	Can automatically truncate outputs exceeding context window, instead of throwing 400 error
Message ID	No message IDs	Each message has its own ID (msg_...)

For the tools:

• Web Search - returns a Markdown list of search results, appears to use Google Search and results are google search links.
• File Search - NOTE: This does not search local files on your machine, you must upload them to OpenAI's vector stores. Documentation.
• Computer Use with sample app that demonstrates how it is actually used. Appears to be a loop that sends screenshot, get suggested actions back, execute action locally, repeat again with the next screenshot.

Output:

• The content in a response in the Responses API can be an array of different outputs and types (with a type parameter):

"content": [
  {
    "type": "output_text",
    "text": "In a peaceful grove beneath a silver moon...",
    "annotations": []
  }

Responses vs Chat Completion API notes:

• instructions is a parameter that essentially replaces the system/developer role messages. When using this parameter with previous_response_id, the Responses API will not carry forward the system/developer messages meaning that we can replace the agent's system message at each turn (which we need to!)
• Use an input parameter (instead of messages) that supports an array of different type objects. This includes the ability to put in a PDF file (which will use their vision model to). Uses their Files API.
• The input parameter can still take a set of messages as we do with the Chat Completion API.
• Simpler way of getting the outputs (no longer have to use choices[0] and they also have an output_text attribute)
• Responses can contain an array of different types (as noted above)
• Ability to only send the latest message and use a previous_response_id
• Reasoning summary available in the output. Including the ability to set the reasoning model effort
• Can force the model to always call at least one tool (tool_choice = required) - could be very useful to ensure that certain agents always call a tool.
• For structured outputs you can now get the Pydantic model directly from the response (response.output[0].content[0].parsed)

Considerations:

• Could have an OpenAI Web Search tool that uses this Responses API's web_search tool (or could add as an option to an existing search tool)
• Similarly, could have an OpenAI File Search tool
• Computer use agent based on sample app.

[marklysze]

@davorrunje, @sonichi - the Responses API has some useful features and could be used to make some tools and agents (noted in description). See full description of issue with differences.