chore: introduce write queue for response_store

# What does this PR do?


## Test Plan

llama_stack/providers/utils/responses/responses_store.py

@@ -3,6 +3,9 @@
 #
 # This source code is licensed under the terms described in the LICENSE file in
 # the root directory of this source tree.
+import asyncio
+from typing import Any
+
 from llama_stack.apis.agents import (
     Order,
 )
@@ -14,25 +17,51 @@ from llama_stack.apis.agents.openai_responses import (
     OpenAIResponseObject,
     OpenAIResponseObjectWithInput,
 )
-from llama_stack.core.datatypes import AccessRule
+from llama_stack.core.datatypes import AccessRule, ResponsesStoreConfig
 from llama_stack.core.utils.config_dirs import RUNTIME_BASE_DIR
+from llama_stack.log import get_logger
 
 from ..sqlstore.api import ColumnDefinition, ColumnType
 from ..sqlstore.authorized_sqlstore import AuthorizedSqlStore
-from ..sqlstore.sqlstore import SqliteSqlStoreConfig, SqlStoreConfig, sqlstore_impl
+from ..sqlstore.sqlstore import SqliteSqlStoreConfig, SqlStoreConfig, SqlStoreType, sqlstore_impl
+
+logger = get_logger(name=__name__, category="responses_store")
 
 
 class ResponsesStore:
-    def __init__(self, sql_store_config: SqlStoreConfig, policy: list[AccessRule]):
-        if not sql_store_config:
-            sql_store_config = SqliteSqlStoreConfig(
+    def __init__(
+        self,
+        config: ResponsesStoreConfig | SqlStoreConfig,
+        policy: list[AccessRule],
+    ):
+        # Handle backward compatibility
+        if not isinstance(config, ResponsesStoreConfig):
+            # Legacy: SqlStoreConfig passed directly as config
+            config = ResponsesStoreConfig(
+                sql_store_config=config,
+            )
+
+        self.config = config
+        self.sql_store_config = config.sql_store_config
+        if not self.sql_store_config:
+            self.sql_store_config = SqliteSqlStoreConfig(
                 db_path=(RUNTIME_BASE_DIR / "sqlstore.db").as_posix(),
             )
-        self.sql_store = AuthorizedSqlStore(sqlstore_impl(sql_store_config))
+        self.sql_store = None
         self.policy = policy
 
+        # Disable write queue for SQLite to avoid concurrency issues
+        self.enable_write_queue = self.sql_store_config.type != SqlStoreType.sqlite
+
+        # Async write queue and worker control
+        self._queue: asyncio.Queue[tuple[OpenAIResponseObject, list[OpenAIResponseInput]]] | None = None
+        self._worker_tasks: list[asyncio.Task[Any]] = []
+        self._max_write_queue_size: int = config.max_write_queue_size
+        self._num_writers: int = max(1, config.num_writers)
+
     async def initialize(self):
         """Create the necessary tables if they don't exist."""
+        self.sql_store = AuthorizedSqlStore(sqlstore_impl(self.sql_store_config))
         await self.sql_store.create_table(
             "openai_responses",
             {
@@ -43,9 +72,70 @@ class ResponsesStore:
             },
         )
 
+        if self.enable_write_queue:
+            self._queue = asyncio.Queue(maxsize=self._max_write_queue_size)
+            for _ in range(self._num_writers):
+                self._worker_tasks.append(asyncio.create_task(self._worker_loop()))
+        else:
+            logger.info("Write queue disabled for SQLite to avoid concurrency issues")
+
+    async def shutdown(self) -> None:
+        if not self._worker_tasks:
+            return
+        if self._queue is not None:
+            await self._queue.join()
+        for t in self._worker_tasks:
+            if not t.done():
+                t.cancel()
+        for t in self._worker_tasks:
+            try:
+                await t
+            except asyncio.CancelledError:
+                pass
+        self._worker_tasks.clear()
+
+    async def flush(self) -> None:
+        """Wait for all queued writes to complete. Useful for testing."""
+        if self.enable_write_queue and self._queue is not None:
+            await self._queue.join()
+
     async def store_response_object(
         self, response_object: OpenAIResponseObject, input: list[OpenAIResponseInput]
     ) -> None:
+        if self.enable_write_queue:
+            if self._queue is None:
+                raise ValueError("Responses store is not initialized")
+            try:
+                self._queue.put_nowait((response_object, input))
+            except asyncio.QueueFull:
+                logger.warning(
+                    f"Write queue full; adding response id={getattr(response_object, 'id', '<unknown>')}"
+                )
+                await self._queue.put((response_object, input))
+        else:
+            await self._write_response_object(response_object, input)
+
+    async def _worker_loop(self) -> None:
+        assert self._queue is not None
+        while True:
+            try:
+                item = await self._queue.get()
+            except asyncio.CancelledError:
+                break
+            response_object, input = item
+            try:
+                await self._write_response_object(response_object, input)
+            except Exception as e:  # noqa: BLE001
+                logger.error(f"Error writing response object: {e}")
+            finally:
+                self._queue.task_done()
+
+    async def _write_response_object(
+        self, response_object: OpenAIResponseObject, input: list[OpenAIResponseInput]
+    ) -> None:
+        if self.sql_store is None:
+            raise ValueError("Responses store is not initialized")
+
         data = response_object.model_dump()
         data["input"] = [input_item.model_dump() for input_item in input]