### 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
method_hint += arg;
						if (use_type_hint) {
							method_hint += ": " + _get_visual_datatype(mi.arguments[i], true, class_name);
						}
					}
				}
				method_hint += ")";
				if (use_type_hint) {
					method_hint += " -> " + _get_visual_datatype(mi.return_val, false, class_name);
				}
				method_hint += ":";
				ScriptLanguage::CodeCompletionOption option(method_hint, ScriptLanguage::CODE_COMPLETION_KIND_FUNCTION);
				options.insert(option.display, option);
			}
		} break;
		case GDScriptParser::COMPLETION_GET_NODE: {
			
			if (p_owner) {
				List<String> opts;
				p_owner->get_argument_options("get_node", 0, &opts);
				for (const String &E : opts) {
					r_forced = true;
					String opt = E.strip_edges();
					if (opt.is_quoted()) {
						
						
						opt = opt.unquote();
					}