How to use date_date_callbacks
The first argument those callbacks get is $element which, essentially, is a render array as described in Render API overview. This means, for example, that a #date_date_callbacks callback could use code similar to the following one.

function mymodule_date_callback($element, $form_state, $date) {
  $element['date']['#attached']['library'][] = 'mymodule/mylibrary';
  // Optionally, the callback can pass values to the JavaScript code.
  $element['date']['#attached']['drupalSettings']['foo'] = 'bar';
}