### 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
ScriptLanguage::CodeCompletionOption option(E->get(), ScriptLanguage::CODE_COMPLETION_KIND_FUNCTION);
		option.insert_text += "(";
		r_result.insert(option.display, option);
	}
	for (const KeyValue<StringName, ProjectSettings::AutoloadInfo> &E : ProjectSettings::get_singleton()->get_autoload_list()) {
		if (!E.value.is_singleton) {
			continue;
		}
		ScriptLanguage::CodeCompletionOption option(E.key, ScriptLanguage::CODE_COMPLETION_KIND_CONSTANT);
		r_result.insert(option.display, option);
	}
	
	for (const KeyValue<StringName, int> &E : GDScriptLanguage::get_singleton()->get_global_map()) {
		ScriptLanguage::CodeCompletionOption option;
		if (ClassDB::class_exists(E.key) || Engine::get_singleton()->has_singleton(E.key)) {
			option = ScriptLanguage::CodeCompletionOption(E.key.operator String(), ScriptLanguage::CODE_COMPLETION_KIND_CLASS);
		} else {
			option = ScriptLanguage::CodeCompletionOption(E.key.operator String(), ScriptLanguage::CODE_COMPLETION_KIND_CONSTANT);
		}
		r_result.insert(option.display, option);
	}
	
	List<StringName> global_classes;
	ScriptServer::get_global_class_list(&global_classes);
	for (const StringName &E : global_classes) {
		ScriptLanguage::CodeCompletionOption option(E, ScriptLanguage::CODE_COMPLETION_KIND_CLASS, ScriptLanguage::LOCATION_OTHER_USER_CODE);
		r_result.insert(option.display, option);
	}
}
static GDScriptCompletionIdentifier _type_from_variant(const Variant &p_value) {