### Godot version

4.1.1

### System information

windows 11

### Issue description

When registering a type with class_name and using that class name to declare a variable in code only, autocomplete works as expected anywhere in other nodes/scenes. However, if making a custom scene node that extends a script with the class_name, if that custom scene is instantiated in a different scene, even if the type is specified, it only shows the parent node's functions and not any of the extended functionality. I have made a basic project showing the issue

### Steps to reproduce

I have made a very simple project showing the issue. https://github.com/mmmmmmmmmmmmmmmmmmmdonuts/godot_4_autocomplete_issue essentially, the extended Node scene will only show the custom function when both the type is specified as well as the type afterwards following "as" 
e.g. `@onready var my_class_4: MyClass = $MyClass4 as MyClass`

### Minimal reproduction project

https://github.com/mmmmmmmmmmmmmmmmmmmdonuts/godot_4_autocomplete_issue
} else {
					Callable::CallError err;
					Variant::construct(base_type.builtin_type, v, nullptr, 0, err);
					if (err.error != Callable::CallError::CALL_OK) {
						break;
					}
				}
				if (v.has_method(p_symbol)) {
					r_result.type = ScriptLanguage::LOOKUP_RESULT_CLASS_METHOD;
					r_result.class_name = Variant::get_type_name(base_type.builtin_type);
					r_result.class_member = p_symbol;
					return OK;
				}
				bool valid = false;
				v.get(p_symbol, &valid);
				if (valid) {
					r_result.type = ScriptLanguage::LOOKUP_RESULT_CLASS_PROPERTY;
					r_result.class_name = Variant::get_type_name(base_type.builtin_type);
					r_result.class_member = p_symbol;
					return OK;
				}
			} break;
			default: {
				base_type.kind = GDScriptParser::DataType::UNRESOLVED;
			} break;
		}
	}
	return ERR_CANT_RESOLVE;
}
::Error GDScriptLanguage::lookup_code(const String &p_code, const String &p_symbol, const String &p_path, Object *p_owner, LookupResult &r_result) {