Use the limited C API for some of our stdlib C extensions

[encukou (Petr Viktorin)]

We’ve reached different personal opinions, so I’ll only answer a part of this post:

@malemburg

FWIW, I don’t think it’s a good idea to tell users: hey, look, you can continue to use the packages released for Python 3.11 with Python 3.12, since the C extension uses the stable ABI, but without actually testing the package with 3.12.

Yet, that’s what happens for most pure-Python libraries. Why should native extensions be different?
PEP 387 applies regardless of stable ABI: if something breaks without deprecation, it’s a bug in CPython (or an explicit exception).

FWIW, a hypothetical PyPI build service won’t help much with this issue. We might need a test service. And/or perhaps metadata that would allow pip to warn “this package wasn’t tested on this version of Python”.