GH-121970: Rewrite the C-API annotations extension

[AA-Turner]

I've tested the output before and after this commit, entirely equal save for a new link target in c-api/module.html#c.Py_mod_create.create_module and c-api/module.html#c.Py_mod_exec.exec_module (because we switch from patching in :noindex: to using the C Domain's supported :no-index-entry:).

This introduces some new dataclasses, removes the state stored in closures and the Annotated class instance, and does some small cleanups. Notably, stable_abi.dat is changed to storing the role name rather than the object type, which simplifies things a little.

A

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📚 Documentation preview 📚: https://cpython-previews--121985.org.readthedocs.build/en/121985/c-api/index.html

• Issue: Improve and reorganise pyspecific #121970

[encukou]

Looks good, thanks for refreshing this extension!

Some nitpicks:

[miss-islington-app]

Thanks @AA-Turner for the PR 🌮🎉.. I'm working now to backport this PR to: 3.12, 3.13.
🐍🍒⛏🤖 I'm not a witch! I'm not a witch!

[miss-islington-app]

Sorry, @AA-Turner, I could not cleanly backport this to 3.13 due to a conflict.
Please backport using cherry_picker on command line.

cherry_picker 22c9d9c1fcc3bb6186524330b169eda6df450f1b 3.13 

[miss-islington-app]

Sorry, @AA-Turner, I could not cleanly backport this to 3.12 due to a conflict.
Please backport using cherry_picker on command line.

cherry_picker 22c9d9c1fcc3bb6186524330b169eda6df450f1b 3.12 

[miss-islington-app]

Thanks @AA-Turner for the PR 🌮🎉.. I'm working now to backport this PR to: 3.12.
🐍🍒⛏🤖

[miss-islington-app]

Sorry, @AA-Turner, I could not cleanly backport this to 3.12 due to a conflict.
Please backport using cherry_picker on command line.

cherry_picker 22c9d9c1fcc3bb6186524330b169eda6df450f1b 3.12 

[bedevere-app]

GH-122025 is a backport of this pull request to the 3.12 branch.

[bedevere-app]

GH-122027 is a backport of this pull request to the 3.13 branch.