gh-114570: Add PythonFinalizationError exception (#115352)

Add PythonFinalizationError exception. This exception derived from
RuntimeError is raised when an operation is blocked during the Python
finalization.

The following functions now raise PythonFinalizationError, instead of
RuntimeError:

* _thread.start_new_thread()
* subprocess.Popen
* os.fork()
* os.fork1()
* os.forkpty()

Morever, _winapi.Overlapped finalizer now logs an unraisable
PythonFinalizationError, instead of an unraisable RuntimeError.

Doc/library/exceptions.rst

@@ -416,6 +416,24 @@ The following exceptions are the exceptions that are usually raised.
    handling in C, most floating point operations are not checked.
 
 
+.. exception:: PythonFinalizationError
+
+   This exception is derived from :exc:`RuntimeError`.  It is raised when
+   an operation is blocked during interpreter shutdown also known as
+   :term:`Python finalization <interpreter shutdown>`.
+
+   Examples of operations which can be blocked with a
+   :exc:`PythonFinalizationError` during the Python finalization:
+
+   * Creating a new Python thread.
+   * :func:`os.fork`.
+
+   See also the :func:`sys.is_finalizing` function.
+
+   .. versionadded:: 3.13
+      Previously, a plain :exc:`RuntimeError` was raised.
+
+
 .. exception:: RecursionError
 
    This exception is derived from :exc:`RuntimeError`.  It is raised when the

Doc/library/sys.rst

@@ -1202,6 +1202,8 @@ always available.
    Return :const:`True` if the main Python interpreter is
    :term:`shutting down <interpreter shutdown>`. Return :const:`False` otherwise.
 
+   See also the :exc:`PythonFinalizationError` exception.
+
    .. versionadded:: 3.5
 
 .. data:: last_exc

Doc/whatsnew/3.13.rst

@@ -160,6 +160,21 @@ Other Language Changes
   (Contributed by Levi Sabah, Zackery Spytz and Hugo van Kemenade in
   :gh:`73965`.)
 
+* Add :exc:`PythonFinalizationError` exception. This exception derived from
+  :exc:`RuntimeError` is raised when an operation is blocked during
+  the :term:`Python finalization <interpreter shutdown>`.
+
+  The following functions now raise PythonFinalizationError, instead of
+  :exc:`RuntimeError`:
+
+  * :func:`_thread.start_new_thread`.
+  * :class:`subprocess.Popen`.
+  * :func:`os.fork`.
+  * :func:`os.forkpty`.
+
+  (Contributed by Victor Stinner in :gh:`114570`.)
+
+
 New Modules
 ===========