[3.13] gh-155894: Fix wait_for() docs claiming a coroutine is wrapped in a Task (#156045)

Author: deadlovelll

Doc/library/asyncio-task.rst

@@ -840,17 +840,13 @@ Timeouts
    Wait for the *aw* :ref:`awaitable <asyncio-awaitables>`
    to complete with a timeout.
 
-   If *aw* is a coroutine it is automatically scheduled as a Task.
-
    *timeout* can either be ``None`` or a float or int number of seconds
    to wait for.  If *timeout* is ``None``, block until the future
    completes.
 
-   If a timeout occurs, it cancels the task and raises
-   :exc:`TimeoutError`.
+   If a timeout occurs, it cancels *aw* and raises :exc:`TimeoutError`.
 
-   To avoid the task :meth:`cancellation <Task.cancel>`,
-   wrap it in :func:`shield`.
+   To prevent *aw* from being cancelled, wrap it in :func:`shield`.
 
    The function will wait until the future is actually cancelled,
    so the total wait time may exceed the *timeout*. If an exception
@@ -891,6 +887,10 @@ Timeouts
    .. versionchanged:: 3.11
       Raises :exc:`TimeoutError` instead of :exc:`asyncio.TimeoutError`.
 
+   .. versionchanged:: 3.12
+      Implemented using :func:`asyncio.timeout`, a coroutine passed as *aw*
+      is no longer wrapped in a :class:`Task` when *timeout* is positive.
+
 
 Waiting primitives
 ==================

Lib/asyncio/tasks.py

@@ -459,15 +459,13 @@ def _release_waiter(waiter, *args):
 async def wait_for(fut, timeout):
     """Wait for the single Future or coroutine to complete, with timeout.
 
-    Coroutine will be wrapped in Task.
-
     Returns result of the Future or coroutine.  When a timeout occurs,
-    it cancels the task and raises TimeoutError.  To avoid the task
-    cancellation, wrap it in shield().
+    it cancels fut and raises TimeoutError.  To prevent fut from being
+    cancelled, wrap it in shield().
 
-    If the wait is cancelled, the task is also cancelled.
+    If the wait is cancelled, fut is also cancelled.
 
-    If the task suppresses the cancellation and returns a value instead,
+    If fut suppresses the cancellation and returns a value instead,
     that value is returned.
 
     This function is a coroutine.