### 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
}
							List<MethodInfo> signals;
							scr->get_script_signal_list(&signals);
							for (const MethodInfo &E : signals) {
								int location = p_recursion_depth + _get_signal_location(scr->get_class_name(), E.name);
								ScriptLanguage::CodeCompletionOption option(E.name, ScriptLanguage::CODE_COMPLETION_KIND_SIGNAL, location);
								r_result.insert(option.display, option);
							}
						}
						HashMap<StringName, Variant> constants;
						scr->get_constants(&constants);
						for (const KeyValue<StringName, Variant> &E : constants) {
							int location = p_recursion_depth + _get_constant_location(scr->get_class_name(), E.key);
							ScriptLanguage::CodeCompletionOption option(E.key.operator String(), ScriptLanguage::CODE_COMPLETION_KIND_CONSTANT, location);
							r_result.insert(option.display, option);
						}
					}
					List<MethodInfo> methods;
					scr->get_script_method_list(&methods);
					for (const MethodInfo &E : methods) {
						if (E.name.begins_with("@")) {
							continue;
						}
						int location = p_recursion_depth + _get_method_location(scr->get_class_name(), E.name);
						ScriptLanguage::CodeCompletionOption option(E.name, ScriptLanguage::CODE_COMPLETION_KIND_FUNCTION, location);
						if (E.arguments.size()) {
							option.insert_text += "(";
						} else {
							option.insert_text += "()";
						}