### 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::class_exists(p_symbol)) {
		r_result.type = ScriptLanguage::LOOKUP_RESULT_CLASS;
		r_result.class_name = p_symbol;
		return OK;
	}
	for (int i = 0; i < Variant::VARIANT_MAX; i++) {
		Variant::Type t = Variant::Type(i);
		if (Variant::get_type_name(t) == p_symbol) {
			r_result.type = ScriptLanguage::LOOKUP_RESULT_CLASS;
			r_result.class_name = Variant::get_type_name(t);
			return OK;
		}
	}