fix: responses <> chat completion input conversion (#3645)

# What does this PR do?

closes #3268
closes #3498

When resuming from previous response ID, currently we attempt to convert
from the stored responses input to chat completion messages, which is
not always possible, e.g. for tool calls where some data is lost once
converted from chat completion message to repsonses input format.

This PR stores the chat completion messages that correspond to the
_last_ call to chat completion, which is sufficient to be resumed from
in the next responses API call, where we load these saved messages and
skip conversion entirely.

Separate issue to optimize storage:
https://github.com/llamastack/llama-stack/issues/3646

## Test Plan
existing CI tests

tests/integration/responses/test_tool_responses.py

@@ -127,6 +127,70 @@ def test_response_non_streaming_file_search_empty_vector_store(compat_client, te
     assert response.output_text
 
 
+def test_response_sequential_file_search(compat_client, text_model_id, tmp_path):
+    """Test file search with sequential responses using previous_response_id."""
+    if isinstance(compat_client, LlamaStackAsLibraryClient):
+        pytest.skip("Responses API file search is not yet supported in library client.")
+
+    vector_store = new_vector_store(compat_client, "test_vector_store")
+
+    # Create a test file with content
+    file_content = "The Llama 4 Maverick model has 128 experts in its mixture of experts architecture."
+    file_name = "test_sequential_file_search.txt"
+    file_path = tmp_path / file_name
+    file_path.write_text(file_content)
+
+    file_response = upload_file(compat_client, file_name, file_path)
+
+    # Attach the file to the vector store
+    compat_client.vector_stores.files.create(
+        vector_store_id=vector_store.id,
+        file_id=file_response.id,
+    )
+
+    # Wait for the file to be attached
+    wait_for_file_attachment(compat_client, vector_store.id, file_response.id)
+
+    tools = [{"type": "file_search", "vector_store_ids": [vector_store.id]}]
+
+    # First response request with file search
+    response = compat_client.responses.create(
+        model=text_model_id,
+        input="How many experts does the Llama 4 Maverick model have?",
+        tools=tools,
+        stream=False,
+        include=["file_search_call.results"],
+    )
+
+    # Verify the file_search_tool was called
+    assert len(response.output) > 1
+    assert response.output[0].type == "file_search_call"
+    assert response.output[0].status == "completed"
+    assert response.output[0].queries
+    assert response.output[0].results
+    assert "128" in response.output_text or "experts" in response.output_text.lower()
+
+    # Second response request using previous_response_id
+    response2 = compat_client.responses.create(
+        model=text_model_id,
+        input="Can you tell me more about the architecture?",
+        tools=tools,
+        stream=False,
+        previous_response_id=response.id,
+        include=["file_search_call.results"],
+    )
+
+    # Verify the second response has output
+    assert len(response2.output) >= 1
+    assert response2.output_text
+
+    # The second response should maintain context from the first
+    final_message = [output for output in response2.output if output.type == "message"]
+    assert len(final_message) >= 1
+    assert final_message[-1].role == "assistant"
+    assert final_message[-1].status == "completed"
+
+
 @pytest.mark.parametrize("case", mcp_tool_test_cases)
 def test_response_non_streaming_mcp_tool(compat_client, text_model_id, case):
     if not isinstance(compat_client, LlamaStackAsLibraryClient):