Mc is a reincarnated soul from the future and is cold and ruthless. He is the son of the emperor but has been secretly planted as a spy since childhood in the prime minister's household as the pm's son. Ml has been told by a prophecy that he will be a great ruler but the mc will be the cause of his death so he should just kill him first.
https://www.novelupdates.com/series/the-elegant-dancing-years/ Is it this!? Tags included are: reincarnation, transmigration, cold protagonist, ancient China, prophecy. There was no mention of post-apocalyptic anywhere or anything to do with zombies.