The video is showing the admin view of the tag info, but it also works for anon and non-staff users. They will see the synonyms, categories where the tags can be used (if they’re restricted to some categories), and tag group names that they belong to (if tag group names are public on the /tags page).
That space is also ready for new features that have been requested, like being able to have descriptions for tags.
I kinda hate the modal approach now, especially since the category modal is so full and keeps growing. Maybe category settings need to be moved out of a modal.