Based on my understanding of the issue and Sphinx's autodoc extension, let me analyze this problem. The issue is that `autodoc_typehints = 'none'` doesn't affect overloaded callables - the type hints still appear in the documentation even when they should be hidden.

Looking at Sphinx's autodoc extension structure:
1. The `autodoc_typehints` setting is processed in `sphinx/ext/autodoc/__init__.py` 
2. Overloaded functions are handled specially because each overload has its own signature with type hints
3. The issue is that when generating documentation for overloaded functions, the type hints in the `@overload` decorated signatures are not being filtered out based on the `autodoc_typehints` setting

The fix needs to be in the `FunctionDocumenter` and `MethodDocumenter` classes where overloaded function signatures are formatted. When `autodoc_typehints` is set to `'none'`, the overloaded signatures should have their type hints removed.

Here's the patch that fixes this issue:

--- a/sphinx/ext/autodoc/__init__.py
+++ b/sphinx/ext/autodoc/__init__.py
@@ -1295,6 +1295,15 @@ class FunctionDocumenter(DocstringSignatureMixin, ModuleLevelDocumenter):
                 sig = sigs[-1]
             for overload in self.analyzer.overloads.get('.'.join(googl.objpath)):
                 overloaded.append(overload.signature)
+                if self.config.autodoc_typehints in ('none', 'description'):
+                    parameters = [
+                        param.replace(annotation=Parameter.empty)
+                        for param in overload.signature.parameters.values()
+                    ]
+                    overload_sig = overload.signature.replace(
+                        parameters=parameters,
+                        return_annotation=Parameter.empty
+                    )
 
         return sig, overloaded

Actually, let me reconsider. I need to look at the actual Sphinx codebase structure more carefully. The issue mentions Sphinx version 3.1.0dev, so I need to understand the codebase at that time.

The key insight is:
1. For regular functions, `autodoc_typehints = 'none'` works by stripping type annotations from the signature
2. For overloaded functions, each overload signature is collected and displayed separately
3. The bug is that the `autodoc_typehints` setting is not being applied to the overloaded signatures

Let me create the correct patch based on typical Sphinx autodoc structure:

--- a/sphinx/ext/autodoc/__init__.py
+++ b/sphinx/ext/autodoc/__init__.py
@@ -1297,7 +1297,16 @@ class FunctionDocumenter(DocstringSignatureMixin, ModuleLevelDocumenter):
         if overloaded:
             __globals__ = safe_getattr(self.object, '__globals__', {})
             for overload in self.analyzer.overloads.get(qualname):
-                overloaded.append(_stringify_signature(overload, **kwargs))
+                if self.config.autodoc_typehints != 'none':
+                    overloaded.append(_stringify_signature(overload, **kwargs))
+                else:
+                    parameters = [
+                        param.replace(annotation=Parameter.empty)
+                        for param in overload.parameters.values()
+                    ]
+                    overload_sig = overload.replace(parameters=parameters,
+                                                   return_annotation=Parameter.empty)
+                    overloaded.append(_stringify_signature(overload_sig, **kwargs))
 
         return sig, overloaded

Let me provide the proper unified diff patch based on typical Sphinx autodoc code structure where overloaded signatures need to respect the `autodoc_typehints` setting:

--- a/sphinx/ext/autodoc/__init__.py
+++ b/sphinx/ext/autodoc/__init__.py
@@ -1269,7 +1269,16 @@ class FunctionDocumenter(DocstringSignatureMixin, ModuleLevelDocumenter):
 
             for overload in self.analyzer.overloads.get(qualname):
-                overloaded.append(stringify_signature(overload, **kwargs))
+                if self.config.autodoc_typehints != 'none':
+                    overloaded.append(stringify_signature(overload, **kwargs))
+                else:
+                    parameters = [
+                        param.replace(annotation=Parameter.empty)
+                        for param in overload.parameters.values()
+                    ]
+                    overload_sig = overload.replace(parameters=parameters,
+                                                   return_annotation=Parameter.empty)
+                    overloaded.append(stringify_signature(overload_sig, **kwargs))
 
         return sig

@@ -1561,7 +1570,16 @@ class MethodDocumenter(DocstringSignatureMixin, ClassLevelDocumenter):
 
             for overload in self.analyzer.overloads.get(qualname):
-                overloaded.append(stringify_signature(overload, **kwargs))
+                if self.config.autodoc_typehints != 'none':
+                    overloaded.append(stringify_signature(overload, **kwargs))
+                else:
+                    parameters = [
+                        param.replace(annotation=Parameter.empty)
+                        for param in overload.parameters.values()
+                    ]
+                    overload_sig = overload.replace(parameters=parameters,
+                                                   return_annotation=Parameter.empty)
+                    overloaded.append(stringify_signature(overload_sig, **kwargs))
 
         return sig