### 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 (_debug_parse_err_line >= 0) {
		return;
	}
	ERR_FAIL_INDEX(p_level, _call_stack.stack_pos);
	int l = _call_stack.stack_pos - p_level - 1;
	GDScriptInstance *instance = _call_stack.levels[l].instance;
	if (!instance) {
		return;
	}
	Ref<GDScript> scr = instance->get_script();
	ERR_FAIL_COND(scr.is_null());
	const HashMap<StringName, GDScript::MemberInfo> &mi = scr->debug_get_member_indices();
	for (const KeyValue<StringName, GDScript::MemberInfo> &E : mi) {
		p_members->push_back(E.key);
		p_values->push_back(instance->debug_get_member_by_index(E.value.index));
	}
}
ScriptInstance *GDScriptLanguage::debug_get_stack_level_instance(int p_level) {