[3.14] gh-158643: Document that Py_EnterRecursiveCall uses the C stack, not a counter (GH-158644) (GH-158654)

(cherry picked from commit d6d1ebc)

Co-authored-by: Bhuvansh <bhuvanshkataria@gmail.com>
Co-authored-by: An Long <aisk@users.noreply.github.com>

Author: 3 people

Doc/c-api/exceptions.rst

@@ -1016,6 +1016,10 @@ because the :ref:`call protocol <call>` takes care of recursion handling.
    case, a :exc:`RecursionError` is set and a nonzero value is returned.
    Otherwise, zero is returned.
 
+   The check is based on the remaining C stack space of the current thread,
+   not on a count of calls, so it is unaffected by
+   :c:func:`Py_SetRecursionLimit` and :func:`sys.setrecursionlimit`.
+
    *where* should be a UTF-8 encoded string such as ``" in instance check"`` to
    be concatenated to the :exc:`RecursionError` message caused by the recursion
    depth limit.
@@ -1026,6 +1030,10 @@ because the :ref:`call protocol <call>` takes care of recursion handling.
    .. versionchanged:: 3.9
       This function is now also available in the :ref:`limited API <limited-c-api>`.
 
+   .. versionchanged:: 3.14
+      The check is based on the remaining C stack space.  Previously, a
+      separate counter of C-level calls was used.
+
 .. c:function:: void Py_LeaveRecursiveCall(void)
 
    Ends a :c:func:`Py_EnterRecursiveCall`.  Must be called once for each