### 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
r_result.class_member = p_symbol;
						return OK;
					}
				}
				if (ClassDB::has_property(class_name, p_symbol, true)) {
					r_result.type = ScriptLanguage::LOOKUP_RESULT_CLASS_PROPERTY;
					r_result.class_name = base_type.native_type;
					r_result.class_member = p_symbol;
					return OK;
				}
				StringName parent = ClassDB::get_parent_class(class_name);
				if (parent != StringName()) {
					base_type.native_type = parent;
				} else {
					base_type.kind = GDScriptParser::DataType::UNRESOLVED;
				}
			} break;
			case GDScriptParser::DataType::BUILTIN: {
				base_type.kind = GDScriptParser::DataType::UNRESOLVED;
				if (Variant::has_constant(base_type.builtin_type, p_symbol)) {
					r_result.type = ScriptLanguage::LOOKUP_RESULT_CLASS_CONSTANT;
					r_result.class_name = Variant::get_type_name(base_type.builtin_type);
					r_result.class_member = p_symbol;
					return OK;
				}
				Variant v;
				Ref<RefCounted> v_ref;
				if (base_type.builtin_type == Variant::OBJECT) {
					v_ref.instantiate();
					v = v_ref;