### 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
int location = p_recursion_depth + _get_method_location(type, E.name);
					ScriptLanguage::CodeCompletionOption option(E.name, ScriptLanguage::CODE_COMPLETION_KIND_FUNCTION, location);
					if (E.arguments.size()) {
						option.insert_text += "(";
					} else {
						option.insert_text += "()";
					}
					r_result.insert(option.display, option);
				}
				return;
			} break;
			case GDScriptParser::DataType::ENUM:
			case GDScriptParser::DataType::BUILTIN: {
				Callable::CallError err;
				Variant tmp;
				Variant::construct(base_type.builtin_type, tmp, nullptr, 0, err);
				if (err.error != Callable::CallError::CALL_OK) {
					return;
				}
				if (!p_only_functions) {
					List<PropertyInfo> members;
					if (p_base.value.get_type() != Variant::NIL) {
						p_base.value.get_property_list(&members);
					} else {
						tmp.get_property_list(&members);
					}
					for (const PropertyInfo &E : members) {
						if (!String(E.name).contains("/")) {
							ScriptLanguage::CodeCompletionOption option(E.name, ScriptLanguage::CODE_COMPLETION_KIND_MEMBER);
							if (GDScriptParser::theme_color_names.has(E.name)) {