Okay, but an alternate universe where Anakin is raised as a Sith by Palpatine, and okay, there are several AUs about that, but an AU where he's raised as both a Sith and a prince by Palpatine is something new.
After the Battle of Naboo, Qui-Gon is dead, Obi-Wan is grieving and unsure what to do, Padmé is busy rebuilding Naboo, the events of The Phantom Menace unfold normally, but with one detail: the council rejects Anakin. They ignore the promise Obi-Wan made on Qui-Gon's deathbed, they reject Obi-Wan's pleas and the fact that Anakin saved Naboo. They want to send him back to Tatooine to be with his mother, as it would be "safer" for the so-called "chosen one" to be away from all the problems he could bring, as well as being too old for training. They put him in a hangar, give him a ticket and a little money, and leave him there to catch a ship to Tatooine.
Okay, so Palpatine is intelligent, he's manipulative, and we can also consider him a bit narcissistic. He's an aristocrat to the core; the way he acts is aristocratic, the way he eats is aristocratic, he smells of old and aristocratic things. So, as an aristocrat, he knows what wealth looks and sounds like to the minority class. So when he sees poor Anakin, a former slave who never had a drop of wealth, he knows exactly where to strike.
He sees the Jedi "returning" a nine-year-old child to his enslaved mother, sees them rejecting a child who was a hero to Naboo, and sees his plans accelerate and take a delicious turn.
Using his contacts, he discovers the hangar where Anakin is and the number of his platform. He approaches him like a grandfather approaches a grandson who has been reprimanded by his mother.
He is understanding, kind, and "caring" in Anakin's eyes, and one of the only people who has been kind to him since he arrived on Coruscant. Anakin doesn't want to bother him, doesn't want to be a problem, that's a fact, and Palpatine doesn't make him feel like a burden. He listens to Anakin, he validates his feelings, he encourages him to vent, and already begins his subtle Sith manipulations, as well as fueling his hatred and resentment against the Jedi.
Following his plan, Palpatine offers Anakin a place where he will be well treated and cared for as his son—not an apprentice, not a protégé, not a pupil, but as a son, because Palpatine knows he can get much more out of a child who has a present and focused father figure than an apprentice who has a master.
Palpatine legally adopts Anakin, and from that day on, he is called Anakin Palpatine, son of Sheev Palpatine. He is not hidden away on Mustafar; he is not merely raised as a Sith apprentice, as a weapon to be used.
He has the finest clothes, the best tutors, the best toys; he has everything good and the best that a slave never had, but the son of an aristocrat now possesses. Palpatine wants to create this sense of security, loyalty, and toxic, distorted love from Anakin for himself—that feeling of: "He is my father, he gave me everything good and the best, he took me in when no one else wanted me, he gave me an opportunity that no one else wanted to give me, i cannot and will not betray him."
Palpatine creates him as both a prince and a weapon, erasing any trace of the boy from Tatooine who once existed and molding him into an heir/prince of his future empire.
Anakin knows proper table manners while also knowing 50 poisons that could simulate death without anyone finding it suspicious. He can discuss politics, philosophy, and sociology with people while simultaneously extracting information from them without them even realizing it.
After the empire, Anakin is the best thing Palpatine ever created and molded. Anakin humanizes him for the political sphere; a chancellor is more likeable if people know he has a family. This type of chancellor receives more votes than a solitary chancellor about whom nobody knows anything. Anakin owes everything, absolutely everything, to Palpatine. He is his father, the man who pulled him out of the gutter, so he can't see the toxic and narcissistic relationship between them.
To him, Palpatine is just a loving father who sometimes criticizes him, knowing that he can do better. While Palpatine doesn't see him as a person, but as a possession, an object that will bring him to his goal, he loves Anakin in his own twisted way, but it's the kind of love a collector has for his favorite piece, knowing that at any moment he can replace it with a new one.