[BUG]: Compatibility issues between pybind11 and Py_LIMITED_API.

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What version (or hash if on master) of pybind11 are you using?

3.0.1

Problem description

I wrote a demo using pybind11 and setuptools to install a function that prints "hello world" for use in Python. However, when I try to make the wheel package support multiple Python versions above 3.10, enabling Py_LIMITED_API results in an error. The error log is in the attachment, along with setup.py and my_extension.cpp.

However, if I compile using the pure Python C API, there are no issues (as shown in the commented section of my_extension.cpp). However, for the actual project I need to build the wheel package, the code is quite complex, and writing it with the pure Python C API is not very practical.

error.log
my_extension.cpp
setup.py

Reproducible example code

Is this a regression? Put the last known working version here if it is.

Not a regression

Start by reproducing the failure with the attached setup.py and my_extension.cpp, then read error.log to identify where Py_LIMITED_API conflicts with pybind11. Compare the failing limited-API build with the commented pure Python C API version. Done means the attached extension can build a wheel for Python versions above 3.10 with Py_LIMITED_API enabled.