gh-150505: document that Pickler and Unpickler are not thread-safe

Sharing Pickler or Unpickler instances across threads has no defined
semantics. The internal state (memo, stream position, stack) forms a
single coherent parse/serialize state that cannot be meaningfully
used across threads simultaneously.

Author: Ahmed Magdy Ali

Doc/library/pickle.rst

@@ -316,6 +316,12 @@ The :mod:`!pickle` module exports three classes, :class:`Pickler`,
    It is an error if *buffer_callback* is not ``None`` and *protocol* is
    ``None`` or smaller than 5.
 
+   .. note::
+      :class:`Pickler` objects are not thread-safe. Sharing a single
+      :class:`Pickler` instance across multiple threads without external
+      synchronization leads to undefined behavior. Use a separate instance
+      per thread.
+
    .. versionchanged:: 3.8
       The *buffer_callback* argument was added.
 
@@ -430,6 +436,12 @@ The :mod:`!pickle` module exports three classes, :class:`Pickler`,
    an :ref:`out-of-band <pickle-oob>` buffer view.  Such buffers have been
    given in order to the *buffer_callback* of a Pickler object.
 
+   .. note::
+      :class:`Unpickler` objects are not thread-safe. Sharing a single
+      :class:`Unpickler` instance across multiple threads without external
+      synchronization leads to undefined behavior. Use a separate instance
+      per thread.
+
    .. versionchanged:: 3.8
       The *buffers* argument was added.
 

Misc/NEWS.d/next/Library/2026-05-29-01-05-14.gh-issue-150505.qOSg_U.rst

@@ -0,0 +1,3 @@
+Document that :class:`pickle.Pickler` and :class:`pickle.Unpickler`
+instances are not thread-safe. Sharing instances across threads without
+external synchronization leads to undefined behavior.