Do not merge: Experiment with Python limited API (take 2)

[astrofrog]

Trying #301 again now that Cython 3.1 is supposed to have good support

[codecov]

Codecov Report

❌ Patch coverage is 29.41176% with 12 lines in your changes missing coverage. Please review.
✅ Project coverage is 90.57%. Comparing base (927912e) to head (b8e5eb5).
⚠️ Report is 126 commits behind head on main.

Files with missing lines	Patch %	Lines
reproject/adaptive/setup_package.py	35.71%	9 Missing ⚠️
reproject/spherical_intersect/setup_package.py	0.00%	3 Missing ⚠️

Additional details and impacted files

@@            Coverage Diff             @@
##             main     #483      +/-   ##
==========================================
- Coverage   91.45%   90.57%   -0.88%     
==========================================
  Files          25       26       +1     
  Lines        1088     1104      +16     
==========================================
+ Hits          995     1000       +5     
- Misses         93      104      +11     

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[astrofrog]

This can be significantly simplified once astropy/extension-helpers#26 is merged

[astrofrog]

Closing in favour of #506