### 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::has_signal(p_class, p_signal)) {
		return ScriptLanguage::LOCATION_OTHER;
	}
	int depth = 0;
	StringName class_test = p_class;
	while (class_test && !ClassDB::has_signal(class_test, p_signal, true)) {
		class_test = ClassDB::get_parent_class(class_test);
		depth++;
	}
	return depth | ScriptLanguage::LOCATION_PARENT_MASK;
}
static int _get_method_location(StringName p_class, StringName p_method) {
	if (!ClassDB::has_method(p_class, p_method)) {
		return ScriptLanguage::LOCATION_OTHER;
	}
	int depth = 0;
	StringName class_test = p_class;
	while (class_test && !ClassDB::has_method(class_test, p_method, true)) {
		class_test = ClassDB::get_parent_class(class_test);
		depth++;
	}
	return depth | ScriptLanguage::LOCATION_PARENT_MASK;
}
static int _get_enum_constant_location(StringName p_class, StringName p_enum_constant) {