Sets the complete ordered list of group ids as currently displayed. order is a reserved path segment matched before /rules/groups/{groupId}, so order is never a valid groupId. Reconciliation: ids in order that still exist are placed in the given order; groups that exist but are missing from order are appended at the end (oldest createdAt first); ids in order that no longer exist are dropped and listed back in notFound - the same name the assign endpoint uses for the same concept. A reorder can never delete, hide, or duplicate a group, but the response order may differ from what was sent - always re-render from the response rather than trusting the sent array.