[Bug]: `playwright.stop()` deadlocks when used with `asyncio-atexit`

[Triconsult]

Version

1.56.0

Steps to reproduce

Run this code:

import asyncio

import asyncio_atexit
import playwright.async_api


async def main():
    async_playwright = await playwright.async_api.async_playwright().start()
    asyncio_atexit.register(lambda: stop_playwright(async_playwright))


async def stop_playwright(async_playwright):
    print("Stopping playwright...")
    await async_playwright.stop()  # Deadlock here
    print("Playwright stopped")


asyncio.run(main())

Expected behavior

The process exits.

Actual behavior

The process deadlocks without ever printing "Playwright stopped".

Additional context

I keep running into this problem because I dislike this pattern where everything async needs to be wrapped in an async with, and I try to abstract it away. I know playwright is primarily designed for testing, but I often find myself using it outside of tests as well, and the constant async with playwright(): quickly gets annoying. (And the repeated starting/stopping is very inefficient.) I'd like to keep playwright running until the program/event loop shuts down, but this bug is preventing me from doing that.

Environment

- Operating System: Windows 11
- CPU: AMD Ryzen 5
- Browser: Irrelevant
- Python Version: 3.13
- Other info: