fix(memory): prevent close() race and enforce closed state in AsyncSQLiteSession

[hsusul]

Please read this first

• Have you read the docs? Yes
• Have you searched for related issues? Yes

Describe the bug

In AsyncSQLiteSession, calling close() concurrently or repeatedly causes an AttributeError: 'NoneType' object has no attribute 'close'.
This occurs because close() checks if self._connection is None: outside self._lock without re-verifying inside async with self._lock:. When two concurrent tasks invoke close(), both pass the initial None check; the first task acquires self._lock, closes self._connection, and sets it to None. When the second task subsequently acquires self._lock, it attempts await self._connection.close() on None.

In addition, AsyncSQLiteSession lacks a self._closed state flag (unlike SQLiteSession). Consequently, calling get_items(), add_items(), pop_item(), or clear_session() after close() re-initializes a new database connection instead of raising RuntimeError("AsyncSQLiteSession is closed").

Debug information

• Agents SDK version: main (0.19.0+)
• Python version: Python 3.13.5
• Operating System: macOS

Repro steps

import asyncio
from agents.extensions.memory import AsyncSQLiteSession

async def main():
    session = AsyncSQLiteSession("test_close_race")
    await session.add_items([{"role": "user", "content": "hi"}])
    # Concurrent close calls raise AttributeError
    await asyncio.gather(session.close(), session.close())

asyncio.run(main())

Expected behavior

AsyncSQLiteSession.close() should be thread-safe, task-safe, and idempotent (subsequent and concurrent calls to close() should be safe no-ops).
Operations invoked on a closed AsyncSQLiteSession should raise RuntimeError("AsyncSQLiteSession is closed"), matching SQLiteSession behavior.

I intend to submit a pull request fixing this issue.