AsyncioIntegration hides an eager task factory from anyio, which breaks anyio task groups #7709

How do you use Sentry?

Sentry Saas (sentry.io)

Version

2.70.0

Steps to Reproduce

Python 3.12 or later, anyio 4.8 or later.

import asyncio

import anyio
import sentry_sdk
from sentry_sdk.integrations.asyncio import AsyncioIntegration


async def child(event):
    await event.wait()


async def main():
    asyncio.get_running_loop().set_task_factory(asyncio.eager_task_factory)
    sentry_sdk.init(integrations=[AsyncioIntegration()])

    async with anyio.create_task_group() as tg:
        tg.start_soon(child, anyio.Event())
        await anyio.sleep(0.01)
        tg.cancel_scope.cancel()


asyncio.run(main())

Expected Result

The task group exits normally, as it does without AsyncioIntegration.

Actual Result

ExceptionGroup: unhandled errors in a TaskGroup (1 sub-exception)
  RuntimeError: Attempted to exit a cancel scope that isn't the current tasks's current cancel scope

Cause

anyio starts the children of a task group non-eagerly, whatever the loop's task factory.
To do that it has to recognise an eager task factory, and asyncio offers no public way to ask.
anyio compares factory.__code__ with asyncio.eager_task_factory.__code__, which every factory returned by asyncio.create_eager_task_factory() shares, and then calls the task constructor from the factory's closure.

AsyncioIntegration replaces the loop's task factory with _sentry_task_factory, a plain function that calls the original.
Its code object is its own, so anyio takes it for an ordinary factory, the child starts eagerly inside create_task(), and anyio's bookkeeping for the task is written after the task has already run.

Proposed fix

When the original factory is an eager one, install a factory built with asyncio.create_eager_task_factory() and wrap the coroutine in its task constructor.
Tasks stay eager, spans are created as before, and anyio recognises the factory.
I have a patch with tests and can open a PR if this approach is acceptable.