### 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 (!opt.replace("/", "_").is_valid_identifier()) {
						
						
						opt = opt.quote(opt.contains("'") ? "\"" : quote_style); 
					}
					ScriptLanguage::CodeCompletionOption option(opt, ScriptLanguage::CODE_COMPLETION_KIND_NODE_PATH);
					options.insert(option.display, option);
				}
				
				for (const KeyValue<StringName, ProjectSettings::AutoloadInfo> &E : ProjectSettings::get_singleton()->get_autoload_list()) {
					String path = "/root/" + E.key;
					ScriptLanguage::CodeCompletionOption option(path.quote(quote_style), ScriptLanguage::CODE_COMPLETION_KIND_NODE_PATH);
					options.insert(option.display, option);
				}
			}
		} break;
		case GDScriptParser::COMPLETION_SUPER_METHOD: {
			if (!completion_context.current_class) {
				break;
			}
			_find_identifiers_in_class(completion_context.current_class, true, false, true, options, 0);
		} break;
	}
	for (const KeyValue<String, ScriptLanguage::CodeCompletionOption> &E : options) {
		r_options->push_back(E.value);
	}
	return OK;
}
#else
Error GDScriptLanguage::complete_code(const String &p_code, const String &p_path, Object *p_owner, List<ScriptLanguage::CodeCompletionOption> *r_options, bool &r_forced, String &r_call_hint) {