bpo-43770: _PyTypes_Init() inits _PyAnextAwaitable_Type (GH-25266)

* Rename PyAnextAwaitable_Type to _PyAnextAwaitable_Type.
* Expose the type in the internal C API.
diff --git a/Objects/object.c b/Objects/object.c
index ceb0990..1224160 100644
--- a/Objects/object.c
+++ b/Objects/object.c
@@ -1833,6 +1833,7 @@ _PyTypes_Init(void)
     INIT_TYPE(PyUnicode_Type);
     INIT_TYPE(PyWrapperDescr_Type);
     INIT_TYPE(Py_GenericAliasType);
+    INIT_TYPE(_PyAnextAwaitable_Type);
     INIT_TYPE(_PyAsyncGenASend_Type);
     INIT_TYPE(_PyAsyncGenAThrow_Type);
     INIT_TYPE(_PyAsyncGenWrappedValue_Type);