gh-106320: Remove private _PyObject C API

Move private _PyObject and private _PyType functions to the internal
C API (pycore_object.h):

* _PyObject_GetMethod()
* _PyObject_IsAbstract()
* _PyObject_NextNotImplemented()
* _PyType_CalculateMetaclass()
* _PyType_GetDocFromInternalDoc()
* _PyType_GetTextSignatureFromInternalDoc()

No longer export these functions.

Include/cpython/object.h

@@ -275,29 +275,17 @@ PyAPI_FUNC(const char *) _PyType_Name(PyTypeObject *);
 PyAPI_FUNC(PyObject *) _PyType_Lookup(PyTypeObject *, PyObject *);
 PyAPI_FUNC(PyObject *) _PyType_LookupId(PyTypeObject *, _Py_Identifier *);
 PyAPI_FUNC(PyObject *) _PyObject_LookupSpecialId(PyObject *, _Py_Identifier *);
-#ifndef Py_BUILD_CORE
-// Backward compatibility for 3rd-party extensions
-// that may be using the old name.
-#define _PyObject_LookupSpecial _PyObject_LookupSpecialId
-#endif
-PyAPI_FUNC(PyTypeObject *) _PyType_CalculateMetaclass(PyTypeObject *, PyObject *);
-PyAPI_FUNC(PyObject *) _PyType_GetDocFromInternalDoc(const char *, const char *);
-PyAPI_FUNC(PyObject *) _PyType_GetTextSignatureFromInternalDoc(const char *, const char *);
 PyAPI_FUNC(PyObject *) PyType_GetModuleByDef(PyTypeObject *, PyModuleDef *);
 PyAPI_FUNC(PyObject *) PyType_GetDict(PyTypeObject *);
 
 PyAPI_FUNC(int) PyObject_Print(PyObject *, FILE *, int);
 PyAPI_FUNC(void) _Py_BreakPoint(void);
 PyAPI_FUNC(void) _PyObject_Dump(PyObject *);
 
-PyAPI_FUNC(int) _PyObject_IsAbstract(PyObject *);
 PyAPI_FUNC(PyObject *) _PyObject_GetAttrId(PyObject *, _Py_Identifier *);
 PyAPI_FUNC(int) _PyObject_SetAttrId(PyObject *, _Py_Identifier *, PyObject *);
 
-PyAPI_FUNC(int) _PyObject_GetMethod(PyObject *obj, PyObject *name, PyObject **method);
-
 PyAPI_FUNC(PyObject **) _PyObject_GetDictPtr(PyObject *);
-PyAPI_FUNC(PyObject *) _PyObject_NextNotImplemented(PyObject *);
 PyAPI_FUNC(void) PyObject_CallFinalizer(PyObject *);
 PyAPI_FUNC(int) PyObject_CallFinalizerFromDealloc(PyObject *);
 

Include/internal/pycore_object.h

@@ -376,7 +376,11 @@ static inline int _PyType_SUPPORTS_WEAKREFS(PyTypeObject *type) {
 }
 
 extern PyObject* _PyType_AllocNoTrack(PyTypeObject *type, Py_ssize_t nitems);
-PyObject *_PyType_NewManagedObject(PyTypeObject *type);
+extern PyObject *_PyType_NewManagedObject(PyTypeObject *type);
+
+extern PyTypeObject* _PyType_CalculateMetaclass(PyTypeObject *, PyObject *);
+extern PyObject* _PyType_GetDocFromInternalDoc(const char *, const char *);
+extern PyObject* _PyType_GetTextSignatureFromInternalDoc(const char *, const char *);
 
 extern int _PyObject_InitializeDict(PyObject *obj);
 int _PyObject_InitInlineValues(PyObject *obj, PyTypeObject *tp);
@@ -432,6 +436,11 @@ extern int _PyObject_IsInstanceDictEmpty(PyObject *);
 
 PyAPI_FUNC(PyObject *) _PyObject_LookupSpecial(PyObject *, PyObject *);
 
+extern int _PyObject_IsAbstract(PyObject *);
+
+extern int _PyObject_GetMethod(PyObject *obj, PyObject *name, PyObject **method);
+extern PyObject* _PyObject_NextNotImplemented(PyObject *);
+
 /* C function call trampolines to mitigate bad function pointer casts.
  *
  * Typical native ABIs ignore additional arguments or fill in missing