### 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
_find_identifiers_in_base(base, false, options, 0);
			}
			r_forced = true;
		} break;
		case GDScriptParser::COMPLETION_RESOURCE_PATH: {
			if (EDITOR_GET("text_editor/completion/complete_file_paths")) {
				_get_directory_contents(EditorFileSystem::get_singleton()->get_filesystem(), options);
				r_forced = true;
			}
		} break;
		case GDScriptParser::COMPLETION_CALL_ARGUMENTS: {
			if (!completion_context.node) {
				break;
			}
			_find_call_arguments(completion_context, completion_context.node, completion_context.current_argument, options, r_forced, r_call_hint);
		} break;
		case GDScriptParser::COMPLETION_OVERRIDE_METHOD: {
			GDScriptParser::DataType native_type = completion_context.current_class->base_type;
			while (native_type.is_set() && native_type.kind != GDScriptParser::DataType::NATIVE) {
				switch (native_type.kind) {
					case GDScriptParser::DataType::CLASS: {
						native_type = native_type.class_type->base_type;
					} break;
					default: {
						native_type.kind = GDScriptParser::DataType::UNRESOLVED;
					} break;
				}
			}
			if (!native_type.is_set()) {
				break;