### 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
String arghint;
	if (!p_is_annotation) {
		arghint += _get_visual_datatype(p_info.return_val, false) + " ";
	}
	arghint += p_info.name + "(";
	int def_args = p_info.arguments.size() - p_info.default_arguments.size();
	int i = 0;
	for (const PropertyInfo &E : p_info.arguments) {
		if (i > 0) {
			arghint += ", ";
		}
		if (i == p_arg_idx) {
			arghint += String::chr(0xFFFF);
		}
		arghint += E.name + ": " + _get_visual_datatype(E, true);
		if (i - def_args >= 0) {
			arghint += String(" = ") + p_info.default_arguments[i - def_args].get_construct_string();
		}
		if (i == p_arg_idx) {
			arghint += String::chr(0xFFFF);
		}
		i++;
	}
	if (p_info.flags & METHOD_FLAG_VARARG) {
		if (p_info.arguments.size() > 0) {