Responses API: Add background parameter support

[leseb]

🚀 Describe the new functionality needed

Add support for the background parameter in the /responses API endpoint (both request and response).

This parameter allows responses to be processed in the background, enabling async processing workflows.

OpenAPI property paths:

• POST.requestBody.content.application/json.properties.background
• POST.responses.200.content.application/json.properties.background

💡 Why is this needed? What if we don't build it?

OpenAI API conformance is crucial for Llama Stack adoption. The background parameter enables async processing patterns that applications may rely on.

Without this parameter:

• Users cannot leverage background processing for long-running responses
• The Responses API conformance score (currently 80.9%) will remain lower than it could be

Other thoughts

Reference: OpenResponses OpenAPI Spec