### 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
arghint += ", ";
		}
		if (p_arg_idx >= p_info.arguments.size()) {
			arghint += String::chr(0xFFFF);
		}
		arghint += "...";
		if (p_arg_idx >= p_info.arguments.size()) {
			arghint += String::chr(0xFFFF);
		}
	}
	arghint += ")";
	return arghint;
}
static String _make_arguments_hint(const GDScriptParser::FunctionNode *p_function, int p_arg_idx) {
	String arghint;
	if (p_function->get_datatype().builtin_type == Variant::NIL) {
		arghint = "void " + p_function->identifier->name.operator String() + "(";
	} else {
		arghint = p_function->get_datatype().to_string() + " " + p_function->identifier->name.operator String() + "(";
	}
	for (int i = 0; i < p_function->parameters.size(); i++) {
		if (i > 0) {
			arghint += ", ";
		}
		if (i == p_arg_idx) {
			arghint += String::chr(0xFFFF);
		}
		const GDScriptParser::ParameterNode *par = p_function->parameters[i];
		if (!par->get_datatype().is_hard_type()) {
			arghint += par->identifier->name.operator String() + ": Variant";