They didn’t end up in some way (no reincarnation whatsoever) but its kinda ambiguous to say since the scene end with a possessed joohwan reaching out to the emperor.
Read here for interesting theory :
https://www.reddit.com/r/boyslove/comments/13nkorh/did_anyone_read_haunted_by_desire/?rdt=54368
In the ending scene side stories ch.15(end) showed that joohwan performing exorcism, calling for Lee Seon the king, right? He then possessed by his previous life/spirit a.k.a Cheonseong & well…. Its all in the topic link above, this reddit user (Livinginfiction473) explained it in details(7 months ago) based on his/her/their theory/understanding but i think its accurate to say it is until(if) the author explain/clear about it later.
God.... I only remember 2 characters.. Like that shaman and the main lead seme... If I remember in previous story shaman and that ghost didn't end up together right??