gh-127791: Fix, document, and test PyUnstable_AtExit (#127793)

Doc/c-api/init.rst

@@ -567,6 +567,15 @@ Initializing and finalizing the interpreter
    customized Python that always runs in isolated mode using
    :c:func:`Py_RunMain`.
 
+.. c:function:: int PyUnstable_AtExit(PyInterpreterState *interp, void (*func)(void *), void *data)
+
+   Register an :mod:`atexit` callback for the target interpreter *interp*.
+   This is similar to :c:func:`Py_AtExit`, but takes an explicit interpreter and
+   data pointer for the callback.
+
+   The :term:`GIL` must be held for *interp*.
+
+   .. versionadded:: 3.13
 
 Process-wide parameters
 =======================

Doc/c-api/sys.rst

@@ -426,3 +426,7 @@ Process Control
    function registered last is called first. Each cleanup function will be called
    at most once.  Since Python's internal finalization will have completed before
    the cleanup function, no Python APIs should be called by *func*.
+
+   .. seealso::
+
+      :c:func:`PyUnstable_AtExit` for passing a ``void *data`` argument.