`RuntimeError: Attempted to exit cancel scope in a different task` when cleaning up multiple MCPClient instances out-of-order

Describe the bug
If two MCPClient objects are instantiated and cleaned up in non-FILO order (i.e., the first-created client is cleaned up before the second), teardown fails with a cascade of RuntimeError/CancelledError exceptions coming from anyio and mcp.client.stdio.

To Reproduce
Minimal repro:

import os, asyncio, json
from typing import Optional
from contextlib import AsyncExitStack
from mcp import ClientSession, StdioServerParameters
from mcp.types import TextContent
from mcp.client.stdio import stdio_client

class MCPClient:
    def __init__(self, command: str, args: list[str], env: Optional[dict] = None):
        self.session: Optional[ClientSession] = None
        self.command, self.args, self.env = command, args, env
        self._cleanup_lock = asyncio.Lock()
        self.exit_stack: Optional[AsyncExitStack] = None

    async def connect_to_server(self):
        await self.cleanup()
        self.exit_stack = AsyncExitStack()

        server_params = StdioServerParameters(
            command=self.command, args=self.args, env=self.env
        )
        stdio_transport = await self.exit_stack.enter_async_context(stdio_client(server_params))
        self.stdio, self.write = stdio_transport
        self.session = await self.exit_stack.enter_async_context(
            ClientSession(self.stdio, self.write)
        )
        await self.session.initialize()

    async def cleanup(self):
        if self.exit_stack:
            async with self._cleanup_lock:
                await self.exit_stack.aclose()
                self.session = None
            self.exit_stack = None

async def main():
    cfg = {
        "command": "npx",
        "args": ["-y", "@adenot/mcp-google-search"],
        "env": {
            "GOOGLE_API_KEY": os.environ["GOOGLE_API_KEY"],
            "GOOGLE_SEARCH_ENGINE_ID": os.environ["GOOGLE_SEARCH_ENGINE_ID"],
        },
    }

    c1, c2 = MCPClient(**cfg), MCPClient(**cfg)
    await c1.connect_to_server()
    await c2.connect_to_server()

    # Works (FILO)
    # await c2.cleanup()
    # await c1.cleanup()

    # Fails (FIFO)
    await c1.cleanup()      # <-- boom
    await c2.cleanup()

if __name__ == "__main__":
    asyncio.run(main())

Expected behavior

cleanup() should succeed regardless of the order in which multiple MCPClient instances are closed, as long as each instance’s own exit_stack is intact. A single client ought to manage its own lifetime without depending on external FILO discipline.

Actual Traceback

RuntimeError: Attempted to exit cancel scope in a different task than it was entered in
...
asyncio.exceptions.CancelledError: Cancelled by cancel scope ...
...
RuntimeError: Attempted to exit a cancel scope that isn't the current task's current cancel scope

Environment

Bắt đầu bằng cách chạy bản tái hiện tối thiểu trong issue, sau đó kiểm tra hành vi của MCPClient.cleanup(), AsyncExitStack, stdio_client và teardown của ClientSession. Bản sửa hoàn tất khi các client được tạo độc lập có thể được dọn dẹp theo thứ tự FIFO mà không xảy ra RuntimeError hoặc CancelledError, đồng thời việc dọn dẹp theo thứ tự FILO vẫn tiếp tục hoạt động.