Basically a Cryo Egeria?
I know the Hyperboreans were aiming for a Nibelung replacement when they created Monomakh, but it does sound like they ended up making a Cryo version of Egeria instead.
Just look at how Egeria is described in the Wings of Merciful, Wrathful Waters:
>When that first heart was removed, the envoy of Celestia, the leader upon whose shoulders lay the duty to create life, came to the great primeval sea, and there she created another heart. That heart had like nobility unto a dragon, but lacked its outer form, and had the majesty of a god, yet was bereft any divine duty. And though it was created by a ruler of humans, its substance and essence were all original matter from this world, entirely without outside elements.
That description maps pretty well onto Monomakh, doesn't it? He's repeatedly said to be of noble blood/birth due to being made from the Cryo Dragon but wasn't shaped like one, had godlike powers but no obvious "divine duty"(he had to go delving in the Shadow Realm to figure out why he was even born), and he was made entirely with materials native to Teyvat. So his existence probably prevented the Cryo Sovereign from being reborn, with that possibly changing during the Cataclysm.
But since is was only Monomakh's soul/consciousness that died and his body remained alive, how would that affect the Cryo Sovereign's reincarnation? They're probably very weak and maybe even indistinguishable from a regular human because Monomakh has been hogging their rightful inheritance even after his consciousness died. And that could mean they've either been reborn and died several times over by now, or they found some external means of prolonging their lifespan.
I really hope we get some clues about the Cryo Sovereign's reincarnation in the next patch. 😭 Neuvillette needs at least one human-shaped Sovereign he can be friends with, come on!