### 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
option.theme_color_name = GDScriptParser::theme_color_names[E.name];
							}
							r_result.insert(option.display, option);
						}
					}
				}
				List<MethodInfo> methods;
				tmp.get_method_list(&methods);
				for (const MethodInfo &E : methods) {
					if (base_type.kind == GDScriptParser::DataType::ENUM && base_type.is_meta_type && !(E.flags & METHOD_FLAG_CONST)) {
						
						continue;
					}
					ScriptLanguage::CodeCompletionOption option(E.name, ScriptLanguage::CODE_COMPLETION_KIND_FUNCTION);
					if (E.arguments.size()) {
						option.insert_text += "(";
					} else {
						option.insert_text += "()";
					}
					r_result.insert(option.display, option);
				}
				return;
			} break;
			default: {
				return;
			} break;
		}
	}
}
static void _find_identifiers(const GDScriptParser::CompletionContext &p_context, bool p_only_functions, HashMap<String, ScriptLanguage::CodeCompletionOption> &r_result, int p_recursion_depth) {