gh-158097: Make test_staggered_race_with_eager_tasks deterministic (#158469)

* gh-158097: Make test_staggered_race_with_eager_tasks deterministic

staggered_race() awaits the coroutines it is given inline, so the
"await asyncio.sleep(0)" in the test's fail() helper suspended the
run_one_coro() task running it and left a scheduled resumption behind.
If the asyncio.sleep(1) winner (started 0.25s late by the stagger delay)
completes before that resumption runs, the winner's cancel() sets
_must_cancel and the resumption throws CancelledError into fail(), so
excs[2] reports a CancelledError instead of a ValueError.

Pending timers are only moved onto the ready queue at the top of
BaseEventLoop._run_once() and are appended after the handles already
queued, so the t=0.50s stagger timer and the t=1.25s sleep(1) timer run
in due-time order.  When both are due in the same _run_once() - which is
what a busy CI machine causes - the stagger timer starts fail(), which
immediately suspends again, and the very next handle is the winner.

Raise straight away instead, so the ValueError is stored in excs[2] in
the same step that starts the coroutine and there is no longer a
scheduled resumption for a cancellation to overtake.  The outcome no
longer depends on the event loop getting another iteration.

* Update Lib/test/test_asyncio/test_eager_task_factory.py

* Delete Misc/NEWS.d/next/Tests/2026-09-30-00-00-00.gh-issue-158097.pcB3mO.rst

---------

Co-authored-by: abhinav-phi <abhinav-phi@users.noreply.github.com>
Co-authored-by: Andrew Svetlov <andrew.svetlov@gmail.com>

Author: abhinav-phi

Lib/test/test_asyncio/test_eager_task_factory.py

@@ -217,7 +217,9 @@ def test_staggered_race_with_eager_tasks(self):
         # See https://github.com/python/cpython/issues/124309
 
         async def fail():
-            await asyncio.sleep(0)
+            # Raise without suspending: staggered_race() cancels unfinished
+            # coroutines once another one wins, so yielding first could turn
+            # this into a CancelledError when the event loop is busy.
             raise ValueError("no good")
 
         async def blocked():