list responses

# What does this PR do?


## Test Plan

llama_stack/providers/utils/responses/responses_store.py

@@ -0,0 +1,98 @@
+# Copyright (c) Meta Platforms, Inc. and affiliates.
+# All rights reserved.
+#
+# This source code is licensed under the terms described in the LICENSE file in
+# the root directory of this source tree.
+from llama_stack.apis.agents import (
+    Order,
+)
+from llama_stack.apis.agents.openai_responses import (
+    ListOpenAIResponseObject,
+    OpenAIResponseInput,
+    OpenAIResponseObject,
+    OpenAIResponseObjectWithInput,
+)
+from llama_stack.distribution.utils.config_dirs import RUNTIME_BASE_DIR
+
+from ..sqlstore.api import ColumnDefinition, ColumnType
+from ..sqlstore.sqlstore import SqliteSqlStoreConfig, SqlStoreConfig, sqlstore_impl
+
+
+class ResponsesStore:
+    def __init__(self, sql_store_config: SqlStoreConfig):
+        if not sql_store_config:
+            sql_store_config = SqliteSqlStoreConfig(
+                db_path=(RUNTIME_BASE_DIR / "sqlstore.db").as_posix(),
+            )
+        self.sql_store = sqlstore_impl(sql_store_config)
+
+    async def initialize(self):
+        """Create the necessary tables if they don't exist."""
+        await self.sql_store.create_table(
+            "openai_responses",
+            {
+                "id": ColumnDefinition(type=ColumnType.STRING, primary_key=True),
+                "created_at": ColumnType.INTEGER,
+                "response_object": ColumnType.JSON,
+                "model": ColumnType.STRING,
+            },
+        )
+
+    async def store_response_object(
+        self, response_object: OpenAIResponseObject, input: list[OpenAIResponseInput]
+    ) -> None:
+        data = response_object.model_dump()
+        data["input"] = [input_item.model_dump() for input_item in input]
+
+        await self.sql_store.insert(
+            "openai_responses",
+            {
+                "id": data["id"],
+                "created_at": data["created_at"],
+                "model": data["model"],
+                "response_object": data,
+            },
+        )
+
+    async def list_responses(
+        self,
+        after: str | None = None,
+        limit: int | None = 50,
+        model: str | None = None,
+        order: Order | None = Order.desc,
+    ) -> ListOpenAIResponseObject:
+        """
+        List responses from the database.
+
+        :param after: The ID of the last response to return.
+        :param limit: The maximum number of responses to return.
+        :param model: The model to filter by.
+        :param order: The order to sort the responses by.
+        """
+        # TODO: support after
+        if after:
+            raise NotImplementedError("After is not supported for SQLite")
+        if not order:
+            order = Order.desc
+
+        rows = await self.sql_store.fetch_all(
+            "openai_responses",
+            where={"model": model} if model else None,
+            order_by=[("created_at", order.value)],
+            limit=limit,
+        )
+
+        data = [OpenAIResponseObjectWithInput(**row["response_object"]) for row in rows]
+        return ListOpenAIResponseObject(
+            data=data,
+            # TODO: implement has_more
+            has_more=False,
+            first_id=data[0].id if data else "",
+            last_id=data[-1].id if data else "",
+        )
+
+    async def get_response_object(self, response_id: str) -> OpenAIResponseObjectWithInput:
+        row = await self.sql_store.fetch_one("openai_responses", where={"id": response_id})
+        if not row:
+            raise ValueError(f"Response with id {response_id} not found") from None
+        return OpenAIResponseObjectWithInput(**row["response_object"])