DLL load failed while importing _tf

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Dear USD community,
when trying to enable the addon, I get the following error message:

Traceback (most recent call last):
  File "C:\Users\peter\Downloads\blender-3.1.2-windows-x64\3.1\scripts\modules\addon_utils.py", line 351, in enable
    mod = __import__(module_name)
  File "C:\Users\peter\AppData\Roaming\Blender Foundation\Blender\3.1\scripts\addons\hdusd\__init__.py", line 108, in <module>
    from . import engine, properties, ui, usd_nodes, mx_nodes, bl_nodes
  File "C:\Users\peter\AppData\Roaming\Blender Foundation\Blender\3.1\scripts\addons\hdusd\engine\__init__.py", line 43, in <module>
    from . import engine, handlers
  File "C:\Users\peter\AppData\Roaming\Blender Foundation\Blender\3.1\scripts\addons\hdusd\engine\engine.py", line 21, in <module>
    from ..utils.stage_cache import CachedStage
  File "C:\Users\peter\AppData\Roaming\Blender Foundation\Blender\3.1\scripts\addons\hdusd\utils\stage_cache.py", line 15, in <module>
    from pxr import Usd
  File "C:\Users\peter\AppData\Roaming\Blender Foundation\Blender\3.1\scripts\addons\hdusd\libs-3.10\lib\python\pxr\Usd\__init__.py", line 24, in <module>
    from pxr import Tf
  File "C:\Users\peter\AppData\Roaming\Blender Foundation\Blender\3.1\scripts\addons\hdusd\libs-3.10\lib\python\pxr\Tf\__init__.py", line 163, in <module>
    PreparePythonModule()
  File "C:\Users\peter\AppData\Roaming\Blender Foundation\Blender\3.1\scripts\addons\hdusd\libs-3.10\lib\python\pxr\Tf\__init__.py", line 88, in PreparePythonModule
    module = importlib.import_module(
  File "C:\Users\peter\Downloads\blender-3.1.2-windows-x64\3.1\python\lib\importlib\__init__.py", line 126, in import_module
    return _bootstrap._gcd_import(name[level:], package, level)
ImportError: DLL load failed while importing _tf: Die angegebene Prozedur wurde nicht gefunden.

I'm on Windows 11, Blender 3.1.2 with the addon in version 1.1.1 built for Blender 3.1.
I also tried the version 1.1.8 with Blender 3.4, but that lead to the identical issue. Setting up the environment with the PYTHONPATH guiding to a different USD installation introduces incompatibilites with Python 3.7 vs. Python 3.10.

Generally this seems like a similar issue to this one: PixarAnimationStudios/OpenUSD#2344
That got resolved by using Python 3.7 and editing the environment variables, but that is not really possible in this case. Do you have a pointer what the issue could be?