Switching between free-threaded and standard ABI does not invalidate build cache

Bug Description

See this bcrypt PR, which fixed a caching issue seen on github actions that led to a segfault. IMO this caching issue should have just led to a rebuild rather than a silently broken build.

Steps to Reproduce

I've only been able to trigger this on bcrypt's CI, but now that I understand what's happening I suspect that if you build PyO3 (or a project that depends on PyO3) with a gil-enabled interpreter and then try to rebuild the project with a free-threaded interpreter but keeping the build cache, you will get a successful build but the python extension will be broken.

Your operating system and version

MacOS

Your Python version (python --version)

3.13.1

Your Rust version (rustc --version)

1.84.0

Your PyO3 version

0.23.4

How did you install python? Did you use a virtualenv?

github actions setup-python action

Additional Info

No response

Start by reproducing the cache reuse described for PyO3 builds when switching between a GIL-enabled and free-threaded Python interpreter, using the bcrypt pull request and GitHub Actions run linked in the issue. Trace which build inputs distinguish the two ABIs, then verify that changing the interpreter mode causes a rebuild rather than reusing an incompatible extension.