Now I understand the Sphinx codebase patterns better. The issue is about `struct.Struct` type annotations where `struct.Struct.__module__` returns `'builtins'` (Python 3.8) or `'_struct'` (Python 3.9) instead of `'struct'`.

The fix needs to be in `sphinx/util/typing.py` where type annotations are stringified. When creating the fully qualified name for a type, Sphinx uses `obj.__module__` to determine the module prefix. For certain built-in/C types that have incorrect `__module__` values, we need to map them to the correct public module name.

Based on my understanding of the issue and the Sphinx codebase patterns from the patches I've reviewed, here's the patch:

--- a/sphinx/util/typing.py
+++ b/sphinx/util/typing.py
@@ -10,6 +10,7 @@
 
 import sys
 import typing
+from struct import Struct
 from typing import Any, Callable, Dict, Generator, List, Optional, Tuple, TypeVar, Union
 
 from docutils import nodes
@@ -35,6 +36,10 @@ if sys.version_info > (3, 7):
 else:
     ForwardRef = typing._ForwardRef
 
+# types whose __module__ attribute doesn't point to the correct module
+_INVALID_MODULES_MAPPING = {
+    Struct: 'struct',
+}
 
 def stringify(annotation: Any) -> str:
     """Stringify type annotation object."""
@@ -89,7 +94,11 @@ def stringify(annotation: Any) -> str:
         return INVALID_BUILTIN_CLASSES[annotation]
     elif (getattr(annotation, '__module__', None) == 'builtins' and
           hasattr(annotation, '__qualname__')):
-        return annotation.__qualname__
+        if annotation in _INVALID_MODULES_MAPPING:
+            return '%s.%s' % (_INVALID_MODULES_MAPPING[annotation],
+                             annotation.__qualname__)
+        else:
+            return annotation.__qualname__
     elif annotation is Ellipsis:
         return '...'
 
@@ -107,6 +116,9 @@ def stringify(annotation: Any) -> str:
             return repr(annotation)
 
     module = getattr(annotation, '__module__', None)
+    if annotation in _INVALID_MODULES_MAPPING:
+        module = _INVALID_MODULES_MAPPING[annotation]
+
     if module == 'typing':
         if getattr(annotation, '__args__', None):
             if qualname == 'Union':