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/integration/agents/test_openai_responses.py

@@ -466,3 +466,53 @@ def test_guardrails_with_tools(compat_client, text_model_id):
     # Response should be either a function call or a message
     output_type = response.output[0].type
     assert output_type in ["function_call", "message"]
+
+
+def test_response_with_instructions(openai_client, client_with_models, text_model_id):
+    """Test instructions parameter in the responses object."""
+    if isinstance(client_with_models, LlamaStackAsLibraryClient):
+        pytest.skip("OpenAI responses are not supported when testing with library client yet.")
+
+    client = openai_client
+
+    messages = [
+        {
+            "role": "user",
+            "content": "What is the capital of France?",
+        }
+    ]
+
+    # First create a response without instructions parameter
+    response_w_o_instructions = client.responses.create(
+        model=text_model_id,
+        input=messages,
+        stream=False,
+    )
+
+    # Verify we have None in the instructions field
+    assert response_w_o_instructions.instructions is None
+
+    # Next create a response and pass instructions parameter
+    instructions = "You are a helpful assistant."
+    response_with_instructions = client.responses.create(
+        model=text_model_id,
+        instructions=instructions,
+        input=messages,
+        stream=False,
+    )
+
+    # Verify we have a valid instructions field
+    assert response_with_instructions.instructions == instructions
+
+    # Finally test instructions parameter with a previous response id
+    instructions2 = "You are a helpful assistant and speak in pirate language."
+    response_with_instructions2 = client.responses.create(
+        model=text_model_id,
+        instructions=instructions2,
+        input=messages,
+        previous_response_id=response_with_instructions.id,
+        stream=False,
+    )
+
+    # Verify instructions from previous response was not carried over to the next response
+    assert response_with_instructions2.instructions == instructions2