### 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;
	if (p_property.type == Variant::NIL) {
		
		return ci;
	}
	if (p_property.usage & (PROPERTY_USAGE_CLASS_IS_ENUM | PROPERTY_USAGE_CLASS_IS_BITFIELD)) {
		ci.enumeration = p_property.class_name;
	}
	ci.type.type_source = GDScriptParser::DataType::ANNOTATED_EXPLICIT;
	ci.type.builtin_type = p_property.type;
	if (p_property.type == Variant::OBJECT) {
		ci.type.kind = GDScriptParser::DataType::NATIVE;
		ci.type.native_type = p_property.class_name == StringName() ? "Object" : p_property.class_name;
	} else {
		ci.type.kind = GDScriptParser::DataType::BUILTIN;
	}
	return ci;
}
#define MAX_COMPLETION_RECURSION 100
struct RecursionCheck {
	int *counter;
	_FORCE_INLINE_ bool check() {
		return (*counter) > MAX_COMPLETION_RECURSION;
	}
	RecursionCheck(int *p_counter) :