### 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
if (!ClassDB::get_integer_constant_enum(p_class, p_enum_constant)) {
		return ScriptLanguage::LOCATION_OTHER;
	}
	int depth = 0;
	StringName class_test = p_class;
	while (class_test && !ClassDB::get_integer_constant_enum(class_test, p_enum_constant, true)) {
		class_test = ClassDB::get_parent_class(class_test);
		depth++;
	}
	return depth | ScriptLanguage::LOCATION_PARENT_MASK;
}
static String _trim_parent_class(const String &p_class, const String &p_base_class) {
	if (p_base_class.is_empty()) {
		return p_class;
	}
	Vector<String> names = p_class.split(".", false, 1);
	if (names.size() == 2) {
		String first = names[0];
		String rest = names[1];
		if (ClassDB::class_exists(p_base_class) && ClassDB::class_exists(first) && ClassDB::is_parent_class(p_base_class, first)) {
			return rest;
		}
	}
	return p_class;
}
static String _get_visual_datatype(const PropertyInfo &p_info, bool p_is_arg, const String &p_base_class = "") {