### 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
r_type = _type_from_variant(scr);
				r_type.type.is_meta_type = true;
				return true;
			}
		}
		return false;
	}
	
	if (GDScriptLanguage::get_singleton()->get_named_globals_map().has(p_identifier->name)) {
		r_type = _type_from_variant(GDScriptLanguage::get_singleton()->get_named_globals_map()[p_identifier->name]);
		return true;
	}
	
	if (ClassDB::class_exists(p_identifier->name) && ClassDB::is_class_exposed(p_identifier->name)) {
		r_type.type.type_source = GDScriptParser::DataType::ANNOTATED_EXPLICIT;
		r_type.type.kind = GDScriptParser::DataType::NATIVE;
		r_type.type.builtin_type = Variant::OBJECT;
		r_type.type.native_type = p_identifier->name;
		r_type.type.is_constant = true;
		if (Engine::get_singleton()->has_singleton(p_identifier->name)) {
			r_type.type.is_meta_type = false;
			r_type.value = Engine::get_singleton()->get_singleton_object(p_identifier->name);
		} else {
			r_type.type.is_meta_type = true;
			r_type.value = Variant();
		}
	}
	return false;
}
static bool _guess_identifier_type_from_base(GDScriptParser::CompletionContext &p_context, const GDScriptCompletionIdentifier &p_base, const StringName &p_identifier, GDScriptCompletionIdentifier &r_type) {