asyncio eager tasks have no awaited_by edge during their first step

Bug report

Bug description:

Task that created by eager task factory runs its first step before the awaited_by edge is registered. During this step the graph shows that this task is awaited by nobody

Repro:

import asyncio

async def child():
    asyncio.print_call_graph()
    await asyncio.sleep(0)

async def main():
    await asyncio.gather(child())

loop = asyncio.new_event_loop()
loop.set_task_factory(asyncio.eager_task_factory)
loop.run_until_complete(main())

Expected:

* Task(name='Task-2', id=0x103544b90)
  + Call stack:
  |   File '/Users/timofeiivankov/cpython/repro.py', line 4, in async child()
  + Awaited by:
    * Task(name='Task-1', id=0x103544d70)
      + Call stack:
      |   File '/Users/timofeiivankov/cpython/repro.py', line 8, in async main()

Actually:

* Task(name='Task-2', id=0x103058b90)
  + Call stack:
  |   File '/Users/timofeiivankov/cpython/repro.py', line 4, in async child()

With the default task factory it works fine as expected

Proposed fix: Register the edge inside the eager start and discard it when the step ends

I have a fix ready

CPython versions tested on:

CPython main branch

Operating systems tested on:

macOS

Linked PRs

• gh-157300

Run the provided asyncio reproduction with eager_task_factory and compare its call graph with the default task factory. Inspect the eager start and awaited_by registration described in the report; done means the first child step shows its parent in the “Awaited by” section without breaking the existing behavior.