### 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.insert_text += "(";
						} else {
							option.insert_text += "()";
						}
						break;
					case GDScriptParser::ClassNode::Member::SIGNAL:
						if (p_only_functions || outer || p_static) {
							continue;
						}
						option = ScriptLanguage::CodeCompletionOption(member.signal->identifier->name, ScriptLanguage::CODE_COMPLETION_KIND_SIGNAL, location);
						break;
					case GDScriptParser::ClassNode::Member::GROUP:
						break; 
					case GDScriptParser::ClassNode::Member::UNDEFINED:
						break;
				}
				r_result.insert(option.display, option);
			}
			outer = true;
			clss = clss->outer;
			classes_processed++;
		}
	}
	
	GDScriptCompletionIdentifier base_type;
	base_type.type = p_class->base_type;
	base_type.type.is_meta_type = p_static;
	_find_identifiers_in_base(base_type, p_only_functions, r_result, p_recursion_depth + 1);
}
static void _find_identifiers_in_base(const GDScriptCompletionIdentifier &p_base, bool p_only_functions, HashMap<String, ScriptLanguage::CodeCompletionOption> &r_result, int p_recursion_depth) {