### 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
GDScriptCompletionIdentifier ci;
	ci.value = p_value;
	ci.type.is_constant = true;
	ci.type.type_source = GDScriptParser::DataType::ANNOTATED_EXPLICIT;
	ci.type.kind = GDScriptParser::DataType::BUILTIN;
	ci.type.builtin_type = p_value.get_type();
	if (ci.type.builtin_type == Variant::OBJECT) {
		Object *obj = p_value.operator Object *();
		if (!obj) {
			return ci;
		}
		ci.type.native_type = obj->get_class_name();
		Ref<Script> scr = p_value;
		if (scr.is_valid()) {
			ci.type.is_meta_type = true;
		} else {
			ci.type.is_meta_type = false;
			scr = obj->get_script();
		}
		if (scr.is_valid()) {
			ci.type.script_type = scr;
			ci.type.kind = GDScriptParser::DataType::SCRIPT;
			ci.type.native_type = scr->get_instance_base_type();
		} else {
			ci.type.kind = GDScriptParser::DataType::NATIVE;
		}
	}
	return ci;
}
static GDScriptCompletionIdentifier _type_from_property(const PropertyInfo &p_property) {