### 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 (identifier_node->next != nullptr && identifier_node->next->type == GDScriptParser::ClassNode::Node::GET_NODE) {
						get_node = static_cast<GDScriptParser::GetNodeNode *>(identifier_node->next);
					}
				} break;
				default: {
				} break;
			}
		} break;
		default: {
		} break;
	}
	if (get_node != nullptr) {
		const Object *node = p_context.base->call("get_node_or_null", NodePath(get_node->full_path));
		if (node != nullptr) {
			if (r_base != nullptr) {
				*r_base = node;
			}
			r_base_type.type_source = GDScriptParser::DataType::ANNOTATED_EXPLICIT;
			r_base_type.kind = GDScriptParser::DataType::NATIVE;
			r_base_type.builtin_type = Variant::OBJECT;
			r_base_type.native_type = node->get_class_name();
			return true;
		}
	}
	return false;
}
static void _find_call_arguments(GDScriptParser::CompletionContext &p_context, const GDScriptParser::Node *p_call, int p_argidx, HashMap<String, ScriptLanguage::CodeCompletionOption> &r_result, bool &r_forced, String &r_arghint) {
	if (p_call->type == GDScriptParser::Node::PRELOAD) {
		if (p_argidx == 0 && bool(EDITOR_GET("text_editor/completion/complete_file_paths"))) {
			_get_directory_contents(EditorFileSystem::get_singleton()->get_filesystem(), r_result);