gh-134455: Fix `build-details.json` to use the ``c_api.headers`` key (#134456)

Fix `build-details.json` generation to use the correct `c_api.headers`
key as defined in PEP 739, instead of `c_api.include`.

Co-authored-by: Filipe Laíns 🇵🇸 <lains@riseup.net>

Misc/NEWS.d/next/Build/2025-05-21-19-46-28.gh-issue-134455.vdwlrq.rst

diff --git a/Misc/NEWS.d/next/Build/2025-05-21-19-46-28.gh-issue-134455.vdwlrq.rst b/Misc/NEWS.d/next/Build/2025-05-21-19-46-28.gh-issue-134455.vdwlrq.rst
new file mode 100644
index 0000000..08833b3
--- /dev/null
+++ b/Misc/NEWS.d/next/Build/2025-05-21-19-46-28.gh-issue-134455.vdwlrq.rst
@@ -0,0 +1,2 @@
+Fixed ``build-details.json`` generation to use the correct ``c_api.headers``
+as defined in :pep:`739`, instead of ``c_api.include``.

Tools/build/generate-build-details.py

diff --git a/Tools/build/generate-build-details.py b/Tools/build/generate-build-details.py
index 5dc100b..87e2620 100644
--- a/Tools/build/generate-build-details.py
+++ b/Tools/build/generate-build-details.py
@@ -123,7 +123,7 @@ def generate_data(schema_version: str) -> collections.defaultdict[str, Any]:
     if has_static_library:
         data['libpython']['static'] = os.path.join(LIBDIR, LIBRARY)
 
-    data['c_api']['include'] = INCLUDEDIR
+    data['c_api']['headers'] = INCLUDEDIR
     if LIBPC:
         data['c_api']['pkgconfig_path'] = LIBPC