[3.14] gh-139806: Mention pickle error changes in What's New in 3.14 (GH-154020) (GH-154162)

The gh-122311 changes made pickle.dump() and pickle.dumps() raise
PicklingError for some failures that previously raised AttributeError,
ImportError, ValueError or UnicodeEncodeError, depending on the
implementation.
Add an entry about this in the "Porting to Python 3.14" section.
(cherry picked from commit eb44708)

Co-authored-by: Serhiy Storchaka <storchaka@gmail.com>
Co-authored-by: Claude Fable 5 <noreply@anthropic.com>

Author: 3 people

Doc/whatsnew/3.14.rst

@@ -3309,6 +3309,16 @@ Changes in the Python API
   This temporary change affects other threads.
   (Contributed by Serhiy Storchaka in :gh:`69998`.)
 
+* :func:`pickle.dump` and :func:`pickle.dumps` now raise
+  :exc:`~pickle.PicklingError` for some failures that previously raised
+  :exc:`AttributeError`, :exc:`ImportError`, :exc:`ValueError`,
+  :exc:`UnicodeEncodeError` or :exc:`!PicklingError`,
+  depending on the implementation
+  (for example, pickling a local object, or an object whose module cannot be imported).
+  The original exception is chained to the :exc:`!PicklingError`.
+  Code that caught these exceptions should also catch :exc:`!PicklingError`.
+  (Contributed by Serhiy Storchaka in :gh:`122311`.)
+
 * :class:`types.UnionType` is now an alias for :class:`typing.Union`,
   causing changes in some behaviors.
   See :ref:`above <whatsnew314-typing-union>` for more details.