### 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
return true;
						case GDScriptParser::ClassNode::Member::GROUP:
							return false; 
						case GDScriptParser::ClassNode::Member::UNDEFINED:
							return false; 
					}
					return false;
				}
				base_type = base_type.class_type->base_type;
				break;
			case GDScriptParser::DataType::SCRIPT: {
				Ref<Script> scr = base_type.script_type;
				if (scr.is_valid()) {
					HashMap<StringName, Variant> constants;
					scr->get_constants(&constants);
					if (constants.has(p_identifier)) {
						r_type = _type_from_variant(constants[p_identifier]);
						return true;
					}
					List<PropertyInfo> members;
					if (is_static) {
						scr->get_property_list(&members);
					} else {
						scr->get_script_property_list(&members);
					}
					for (const PropertyInfo &prop : members) {
						if (prop.name == p_identifier) {
							r_type = _type_from_property(prop);
							return true;
						}