To be clear on this, Einhart is a descendant of, and has the memories of, the Hegemon Klaus Ingvalt; Vivio is a clone, with little to no memory transference, of the Sankt Kaiser Olivie Sägebrecht.
(I'd also say that the recording seems less like they intentionally made a sex tape, and more that, since they seem to have started while wearing their barrier jackets, either Raising Heart or Bardiche were accidentally still in recording mode from the training.)