azure-ai-agentserver: Support background mode and resumable streaming for hosted agents

[niallkeys]

Feature Request

Support background: true and resumable streaming (GET /responses/{id}?stream=true&starting_after=N) for hosted agents, matching the behavior already available for direct model invocations via the Foundry Responses API.

Current Behavior

Direct model invocation (works)

When calling the Responses API directly with a model deployment:

POST /openai/responses
{
  "model": "gpt-4o",
  "stream": true,
  "store": true,
  "background": true,
  "input": [{"role": "user", "content": "Hello"}]
}

• Returns immediately with status: "in_progress" and "background": true
• Every SSE event includes a sequence_number
• GET /responses/{id}?stream=true&starting_after=0 replays all stored events, then continues with live events if still in progress
• Response lifecycle completes correctly (status: "completed", output populated)

Hosted agent invocation (does not work)

When calling the same Responses API with an agent_reference pointing to a hosted agent:

POST /openai/responses
{
  "model": "gpt-5",
  "stream": true,
  "store": true,
  "background": true,
  "agent_reference": {"type": "agent_reference", "name": "my-agent"},
  "input": [{"role": "user", "content": "Hello"}]
}

• Returns immediately with status: "in_progress" but the stored response has "background": false — the flag is silently dropped
• GET /responses/{id}?stream=true&starting_after=0 returns "Streaming is not enabled for this response"
• The response object remains stuck at status: "in_progress" with empty output, even after the agent completes and conversation items are saved
• The azure-ai-agentserver-core SDK (v1.0.0b16) has no reference to background anywhere in its source

Why This Matters

The primary use case is resumable/rejoinable streaming for chat UIs. When a user:

• Refreshes the page mid-generation
• Loses network connectivity temporarily
• Opens a conversation that is still being generated in another tab

They should be able to call GET /responses/{id}?stream=true&starting_after=0 to replay past events and continue receiving live events. This works today for direct model calls but not for hosted agents, despite both using the same /openai/responses API surface.

Observations

• The SDK already assigns sequence_number to every ResponseStreamEvent via StreamEventState — the primitive for starting_after resumption is already in place
• The SDK already supports store=true which saves completed items to the Conversations API after stream completion
• The gap appears to be in Foundry's proxy layer between the Responses API endpoint and the hosted agent container — it doesn't buffer/store SSE events as they pass through for hosted agents the way it does for direct model calls

Expected Behavior

background: true + stream: true should work identically for hosted agents as it does for direct model calls:

1. Foundry buffers SSE events as they pass through from the hosted agent container
2. GET /responses/{id}?stream=true&starting_after=N replays stored events and continues with live events
3. The response lifecycle completes correctly when the agent finishes

Environment

• azure-ai-agentserver-core==1.0.0b16
• azure-ai-agentserver-langgraph==1.0.0b16
• API version: 2025-11-15-preview