I created a new branch in my clone for you that has the 3.10 workaround disabled.

# checkout:
git clone -b bpo45319 https://github.com/tiran/wrapt.git
cd wrapt

# build src/wrapt/_wrappers.abi3.so
python3 setup.py build_ext -i

# run tests
$ PYTHONPATH=src python3.9 tests/test_update_attributes.py 
..........
----------------------------------------------------------------------
Ran 10 tests in 0.001s

OK

$ PYTHONPATH=src python3.10 tests/test_update_attributes.py 
FF........
======================================================================
FAIL: test_update_annotations (__main__.TestUpdateAttributes)
----------------------------------------------------------------------
Traceback (most recent call last):
  File "/tmp/wrapt/tests/test_update_attributes.py", line 149, in test_update_annotations
    self.assertEqual(function.__wrapped__.__annotations__, override_annotations)
AssertionError: {} != {'override_annotations': ''}
- {}
+ {'override_annotations': ''}

======================================================================
FAIL: test_update_annotations_modified_on_original (__main__.TestUpdateAttributes)
----------------------------------------------------------------------
Traceback (most recent call last):
  File "/tmp/wrapt/tests/test_update_attributes.py", line 173, in test_update_annotations_modified_on_original
    self.assertEqual(function.__annotations__, override_annotations)
AssertionError: {} != {'override_annotations': ''}
- {}
+ {'override_annotations': ''}

----------------------------------------------------------------------
Ran 10 tests in 0.001s

FAILED (failures=2)