With V. Kalvakota, we wrote an essay pointing out the traditional points of holography where we have contrasted the case for AdS and de Sitter. The latter has points that are non-trivial in these traditional senses, so people have looked out for answers in different holographic settings. This paper was written for GRF 2024.
(Some may find this review we wrote last year helpful along with this reading.)
But isn't entanglement entropy well-defined in de Sitter? The group here with takayanagi worked on many good field theoretic aspects of dS, including perturbed CFT calculations, AdS/BCFT, things with gapped phases and Janus solutions; at the end of the day double Wick rotations are not a bad thing, are they? I might be missing a lot though since I'm not in high energy theory.