Palpatine is relaxed, confident, patient. Like a spider. His scheme has multiple stages and layers. It doesn't have a sell-by date, nor is it dependent on every single thing going exactly as he'd envisioned back when he was gaming things out. For instance, he didn't plan for the sudden appearance of a possible "Chosen One," Anakin Skywalker, brought to Coruscant via Tatooine and Naboo by a Jedi who has trouble following protocol. Still, he barely misses a step, telling the boy hero at the end of "The Phantom Menace" that "we will watch your career with great interest."
Anakin is instrumental in helping him dissolve the Senate, end democracy, and proclaim himself supreme ruler of the galaxy. It takes a truly formidable villain to see his incipient scheme to rule the galaxy being complicated early in the process by the arrival of a possible messiah figure who's under the tutelage of his mortal enemies, the Jedi Council, and fold the kid into the plan, not immediately, but over the course of about ten years.
Palpatine draws Anakin into his fold by playing on his fears that, despite his Jedi powers, he's unable to prevent loved ones from dying. Anakin is specifically worried about Padme, whom he pictured dying in childbirth during one of his nightmares. But he's also traumatized by the death of his mother at the hands of Tusken raiders in the previous movie. Palpatine promises Anakin that he'll teach him a secret Sith power that can defeat death itself and that only one Sith, Plagueis the Wise, knew how to use it.
Some have argued the main plot of "The Rise of Skywalker," wherein "somehow Palpatine has returned," was planted in, and is justified by, the scene in "Sith" where Palpatine tells the story of Plagueis the Wise. I don't want to get into all the reasons why I don't accept "Rise of Skywalker" as a legitimate "Star Wars" film (the short version: it's the only one of the big nine that seems to have been manufactured entirely from negative, petty impulses). So let's just say that Palpatine is so brilliant and diabolical that I wouldn't rule out the possibility that he'd gamed out, "What would I do if somebody killed me?" Palpatine seems quite smug as he tells Anakin, "to cheat death is a power only one has achieved"; he likely wasn't talking about the master, but the apprentice, who killed the master in his sleep after learning everything he knew.
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