I have the impression they were “added” recently. I am quite sure they were not there when I wrote Admin.groups.manage.membership.automatic not replaced - #6 by Moin.
But maybe it’s related to the changes there. In FIX: Allow anyone who can manage groups to see Automatic tooltip by martin-brennan · Pull Request #30174 · discourse/discourse · GitHub, checks whether the group is an automatic group have been removed.
canManageGroup is used in discourse/app/assets/javascripts/discourse/app/templates/group-index.hbs at main · discourse/discourse · GitHub to decide whether to show those buttons or not.