How to get the enabled manage displays per node type?
You can use this service:

EntityDisplayRepository


  Provides a repository for entity display objects (view modes and form
  modes).


Example:

$view_modes = \Drupal::service('entity_display.repository')
  -&gt;getViewModeOptionsByBundle('node', 'article');


More info: https://api.drupal.org/api/drupal/core%21lib%21Drupal%21Core%21Entity%21EntityDisplayRepository.php/class/EntityDisplayRepository/8.2.x