Unclosed client session when using some litellm models

[lvicentesanchez]

Describe the bug

When using the litellm extension with models like gemini/gemini-2.5-flash or anthropic/... you get the following message when the app finishes:

Unclosed client session
client_session: <aiohttp.client.ClientSession object at 0x7fd44a73b890>
Unclosed connector
connections: ['deque([(<aiohttp.client_proto.ResponseHandler object at 0x7fd44a7034d0>, 9465.214257948)])']
connector: <aiohttp.connector.TCPConnector object at 0x7fd449d71610>

Debug information

• Agents SDK version: (e.g. v0.0.3)
• Python version (e.g. Python 3.10)

Repro steps

import asyncio
import os

from agents import (
    Agent,
    ModelSettings,
    Runner,
    set_tracing_disabled,
)
from agents.extensions.models.litellm_model import LitellmModel
from dotenv import load_dotenv

set_tracing_disabled(True)
load_dotenv(override=True)


agent = Agent(
    name="Trivia assistant",
    instructions="You are a helpful and informative trivia assistant.",
    model=LitellmModel(
        model="gemini/gemini-2.5-flash",
        api_key=os.getenv("GEMINI_API_KEY"),
    ),
    model_settings=ModelSettings(temperature=0.2, top_p=0.95),
)


async def main():
    result = await Runner.run(
        agent,
        input=(
            "Calculate how long it takes to the fastest land animal to run through the longest continuous road. "
            "Only take into account roads without gaps or interruptions."
        ),
    )
    print(result.final_output)


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

Expected behavior

As with other models supported by litellm, we shouldn't seen this message.