feat: OpenAI Responses API (#1989)

# What does this PR do?

This provides an initial [OpenAI Responses
API](https://platform.openai.com/docs/api-reference/responses)
implementation. The API is not yet complete, and this is more a
proof-of-concept to show how we can store responses in our key-value
stores and use them to support the Responses API concepts like
`previous_response_id`.

## Test Plan

I've added a new
`tests/integration/openai_responses/test_openai_responses.py` as part of
a test-driven development for this new API. I'm only testing this
locally with the remote-vllm provider for now, but it should work with
any of our inference providers since the only API it requires out of the
inference provider is the `openai_chat_completion` endpoint.

```
VLLM_URL="http://localhost:8000/v1" \
INFERENCE_MODEL="meta-llama/Llama-3.2-3B-Instruct" \
llama stack build --template remote-vllm --image-type venv --run
```

```
LLAMA_STACK_CONFIG="http://localhost:8321" \
python -m pytest -v \
  tests/integration/openai_responses/test_openai_responses.py \
  --text-model "meta-llama/Llama-3.2-3B-Instruct"
 ```

---------

Signed-off-by: Ben Browning <bbrownin@redhat.com>
Co-authored-by: Ashwin Bharambe <ashwin.bharambe@gmail.com>

tests/integration/test_cases/openai/responses.json

@@ -0,0 +1,37 @@
+{
+  "non_streaming_01": {
+    "data": {
+      "question": "Which planet do humans live on?",
+      "expected": "Earth"
+    }
+  },
+  "non_streaming_02": {
+    "data": {
+      "question": "Which planet has rings around it with a name starting with letter S?",
+      "expected": "Saturn"
+    }
+  },
+  "streaming_01": {
+    "data": {
+      "question": "What's the name of the Sun in latin?",
+      "expected": "Sol"
+    }
+  },
+  "streaming_02": {
+    "data": {
+      "question": "What is the name of the US captial?",
+      "expected": "Washington"
+    }
+  },
+  "tools_web_search_01": {
+    "data": {
+      "input": "How many experts does the Llama 4 Maverick model have?",
+      "tools": [
+        {
+          "type": "web_search"
+        }
+      ],
+      "expected": "128"
+    }
+  }
+}

tests/integration/test_cases/test_case.py

@@ -12,6 +12,7 @@ class TestCase:
     _apis = [
         "inference/chat_completion",
         "inference/completion",
+        "openai/responses",
     ]
     _jsonblob = {}