How do I add a custom sorting variable to a view?
Have you created a custom theme, or are you using a contrib theme?  If you have created a custom subtheme, then you can override the template for this particular view at the appropriate level (e.g. something like views-view-fields.xxx.yyy.twig) and then you can implement custom logic that tests if that particular field is greater than today's date, and then inject a CSS class, or change the markup, etc.

If are not subtheming or just don't want to go down that road, you can do as you suggested and have a "Featured field".  There is a module called Computed Fields (which helps you create derived fields, essentially) which may facilitate you doing this: https://www.drupal.org/project/computed_field.  I've not tried it myself for your particular use case, but it may be worth exploring.