### 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
}
						options.insert(option.display, option);
					}
				}
			}
		} break;
		case GDScriptParser::COMPLETION_INHERIT_TYPE: {
			_list_available_types(true, completion_context, options);
			r_forced = true;
		} break;
		case GDScriptParser::COMPLETION_TYPE_NAME_OR_VOID: {
			ScriptLanguage::CodeCompletionOption option("void", ScriptLanguage::CODE_COMPLETION_KIND_PLAIN_TEXT);
			options.insert(option.display, option);
		}
			[[fallthrough]];
		case GDScriptParser::COMPLETION_TYPE_NAME: {
			_list_available_types(false, completion_context, options);
			r_forced = true;
		} break;
		case GDScriptParser::COMPLETION_PROPERTY_DECLARATION_OR_TYPE: {
			_list_available_types(false, completion_context, options);
			ScriptLanguage::CodeCompletionOption get("get", ScriptLanguage::CODE_COMPLETION_KIND_PLAIN_TEXT);
			options.insert(get.display, get);
			ScriptLanguage::CodeCompletionOption set("set", ScriptLanguage::CODE_COMPLETION_KIND_PLAIN_TEXT);
			options.insert(set.display, set);
			r_forced = true;
		} break;
		case GDScriptParser::COMPLETION_PROPERTY_DECLARATION: {
			ScriptLanguage::CodeCompletionOption get("get", ScriptLanguage::CODE_COMPLETION_KIND_PLAIN_TEXT);
			options.insert(get.display, get);