Test pickling a simple callable (does not work). (#3906)

* Test pickling a simple callable (does not work).

Currently only documents that it does not work. Starting point for future fix.

* Use re.search to accommodate variations of the TypeError message.

* PyPy: exercise full dumps/loads cycle.

* Adding explicit "broken" comment.

tests/test_pickling.py

@@ -1,4 +1,5 @@
 import pickle
+import re
 
 import pytest
 
@@ -6,6 +7,20 @@ import env
 from pybind11_tests import pickling as m
 
 
+def test_pickle_simple_callable():
+    assert m.simple_callable() == 20220426
+    if env.PYPY:
+        serialized = pickle.dumps(m.simple_callable)
+        deserialized = pickle.loads(serialized)
+        assert deserialized() == 20220426
+    else:
+        # To document broken behavior: currently it fails universally with
+        # all C Python versions.
+        with pytest.raises(TypeError) as excinfo:
+            pickle.dumps(m.simple_callable)
+        assert re.search("can.*t pickle .*PyCapsule.* object", str(excinfo.value))
+
+
 @pytest.mark.parametrize("cls_name", ["Pickleable", "PickleableNew"])
 def test_roundtrip(cls_name):
     cls = getattr(m, cls_name)