This is how a form widget looks like for a vocabulary with nested terms, when configured to be rendered as a checkbox list:

For D7, you can use the Taxonomy Term Reference Tree Widget module to improve how this widget works, but I believe that all the bell and whistles it offers would be too much for core. We should just get rid of the dashes from the checkbox labels and add indentation to the checkboxes. It would be so much better and more readable like so:

Related: https://drupal.stackexchange.com/questions/85011/how-to-get-rid-of-the-s... https://drupal.stackexchange.com/questions/121053/add-class-to-sub-taxon... https://www.drupal.org/project/drupal/issues/648264 (Core taxonomy.module issue, pending since 2009 - although for dropdowns)
Recent comments
@yorkshirepudding, In the end I fixed it by deleting the config/active folder contents, copying the config/staging/ files into config/active, importing the database again and clearing the caches...
Importing the staged config throws an error: another field with the same name already exists
Thanks, I have to go out now, I will try later on and report back
Importing the staged config throws an error: another field with the same name already exists
Hi Francis. Yes, what config do you have in staging for it? You might have configs like: field.field.field_video_embed field.instance.node.page....
Importing the staged config throws an error: another field with the same name already exists