Radio button in Drupal 8
if you look at /core/lib/Drupal/Core/Render/Element/Radios.php  you'll see it's not a render element, but a form element.

You can't use it without putting it in a form. If you search the code base for extends FormBase, you'll see many examples of forms that you can start from in building your own form, many of them quite simple.

For example:
/core/modules/system/tests/modules/form_test/src/Form/FormTestProgrammaticForm.php