feat: Add instructions parameter in response object (#3741)

# Problem
The current inline provider appends the user provided instructions to
messages as a system prompt, but the returned response object does not
contain the instructions field (as specified in the OpenAI responses
spec).

# What does this PR do?
This pull request adds the instruction field to the response object
definition and updates the inline provider. It also ensures that
instructions from previous response is not carried over to the next
response (as specified in the openAI spec).

Closes #[3566](https://github.com/llamastack/llama-stack/issues/3566)

## Test Plan

- Tested manually for change in model response w.r.t supplied
instructions field.
- Added unit test to check that the instructions from previous response
is not carried over to the next response.
- Added integration tests to check instructions parameter in the
returned response object.
- Added new recordings for the integration tests.

---------

Co-authored-by: github-actions[bot] <github-actions[bot]@users.noreply.github.com>

tests/unit/providers/agents/meta_reference/test_openai_responses.py

@@ -814,6 +814,69 @@ async def test_create_openai_response_with_instructions_and_previous_response(
     assert sent_messages[3].content == "Which is the largest?"
 
 
+async def test_create_openai_response_with_previous_response_instructions(
+    openai_responses_impl, mock_responses_store, mock_inference_api
+):
+    """Test prepending instructions and previous response with instructions."""
+
+    input_item_message = OpenAIResponseMessage(
+        id="123",
+        content="Name some towns in Ireland",
+        role="user",
+    )
+    response_output_message = OpenAIResponseMessage(
+        id="123",
+        content="Galway, Longford, Sligo",
+        status="completed",
+        role="assistant",
+    )
+    response = _OpenAIResponseObjectWithInputAndMessages(
+        created_at=1,
+        id="resp_123",
+        model="fake_model",
+        output=[response_output_message],
+        status="completed",
+        text=OpenAIResponseText(format=OpenAIResponseTextFormat(type="text")),
+        input=[input_item_message],
+        messages=[
+            OpenAIUserMessageParam(content="Name some towns in Ireland"),
+            OpenAIAssistantMessageParam(content="Galway, Longford, Sligo"),
+        ],
+        instructions="You are a helpful assistant.",
+    )
+    mock_responses_store.get_response_object.return_value = response
+
+    model = "meta-llama/Llama-3.1-8B-Instruct"
+    instructions = "You are a geography expert. Provide concise answers."
+
+    mock_inference_api.openai_chat_completion.return_value = fake_stream()
+
+    # Execute
+    await openai_responses_impl.create_openai_response(
+        input="Which is the largest?", model=model, instructions=instructions, previous_response_id="123"
+    )
+
+    # Verify
+    mock_inference_api.openai_chat_completion.assert_called_once()
+    call_args = mock_inference_api.openai_chat_completion.call_args
+    params = call_args.args[0]
+    sent_messages = params.messages
+
+    # Check that instructions were prepended as a system message
+    # and that the previous response instructions were not carried over
+    assert len(sent_messages) == 4, sent_messages
+    assert sent_messages[0].role == "system"
+    assert sent_messages[0].content == instructions
+
+    # Check the rest of the messages were converted correctly
+    assert sent_messages[1].role == "user"
+    assert sent_messages[1].content == "Name some towns in Ireland"
+    assert sent_messages[2].role == "assistant"
+    assert sent_messages[2].content == "Galway, Longford, Sligo"
+    assert sent_messages[3].role == "user"
+    assert sent_messages[3].content == "Which is the largest?"
+
+
 async def test_list_openai_response_input_items_delegation(openai_responses_impl, mock_responses_store):
     """Test that list_openai_response_input_items properly delegates to responses_store with correct parameters."""
     # Setup