Honestly, a lot of what the Emperor does is less explainable less by Sith Lord powers...or philosophy...and is more that he's basically a malignant narcissist with wizard powers, the creepy uncle of the entire Galaxy Long Ago and Far Far Away.
Palpatine has an abusive relationship with Darth Vader: he chanced on a kid with emotional baggage and made that baggage as painful as possible while also isolating that kid from real sources of validity and love...then he pushed that kid to do something so unforgivable that there seemed to be no way back. If Anakin burned to death he would have just found a replacement, like how he replaced Maul, et al. Vader is perfectly isolated in a way that make him the perfect subject for a power/control freak like Palpatine: always in physical pain; always isolated from literal contact by his suit and social contact by his position as Aloof Magic Homicidal Authority Figure; constantly reminded of what he's lost. Vader might hate and resent Palpatine all along, but he's dependent on him in a way that makes Palpatine feel safe and in control.
In Luke, Vader see the possibility of connection to another person--being de facto already connected through bloodline and Force sensitivity--but we watch Vader try to replicate the dynamic he has with Palpatine: he coerces his son, hurts his son, then offers alliance in a way that commands deference and is structured entirely in terms of using their shared power to dominate others...and Luke decides he'd rather die than say "yes."
Palpatine speaks with Vader about Luke as "Skywalker's son"--creating semantic distance, communicating that Darth Vader isn't Anakin, doesn't get to acknowledge the family connection. We're not actually show his visions, so within the frame of the scene when Palpatine speaks of forseeing stuff it's not objectively true that he forsees or that he's interpreting or communicating accurately what he sees. It is entirely possible to read his proclamations as utterances of want and intent matching his narcissism, with no mysticism: he's afraid of Luke because he's a challenge to his power in general and to his power over Vader specifically and therefore wants Luke both not a Jedi and dead, and ideally wants Vader to kill him because that re-affirms their power-control abuse dynamic. When he's crafted another coercive scenario and can imagine replacing Vader with Luke, he can "see" that too.
The throneroom scene can be read as an interaction about power and cruelty as psychological forces entirely separate from the Force powers underpinning the three participants.
Palpatine has created what he sees as a let's-you-and-him fight scenario where he wins, and gets his validation, either way. Vader kills Luke: Palpatine keeps his already-broken partner. If Luke kills Vader, Palpatine imagines that he can leverage Luke into a position of submission through carrot and stick because, well...he's done this over and over, using carrots and sticks to create wounded child-adults that can't stand against him, and also has enough concealed mojo to kill Luke outright. When he discerns Leia--who is an ideal lever with which to move Luke or Vader, and also a Third Option of who to break and reassemble deliberately-damaged--he gets downright perky. When Vader loses and Luke won't play the scenario out to the intended finish, Palpatine doesn't just kill Luke for defiance, he loses his bottle and deliberately hurts him over and over while cackling. Anything except another loop of the same abuse dynamic is unacceptable.
That whole bit about "strike me down in anger"? Set aside the mysticism and its a psychological tactic that digs at the center of Luke--he is terrified of being his dad or mirroring his dad's path of descent--and also just a universal tactic of the amoral--using the morality of a moral person pushed to violence against them by twisting the scenario--and also just a straight up bluff--the kind of thing a vain old creep would say just to impose the veneer of control on a situation: "I meant to do that." It also an inversion of Kenobi's end--resigning to death, passing on his burden to Luke, rising above the moment even as Vader demands death-as-ultimate-deference. The Emperor is 100% selfish trash and nobody matters but him, even if he's dead that was the plan and he wins because he says, nyah, nyah. The way he actually dies--tossed in a pit by a man he felt he owned to defend a son that Palpatine tried to first groom, then murder--demonstrates how hollow his confidence was, and how shallow his control--of Vader, of the galaxy--was.
When Luke calls Vader a both "my father" and "a Jedi Knight" it's a form of unconditional validation, directly contrasted with the Emperor bodily demonstrating that he's only got one move--parasitically ride people until they're useless, then find another person to break with and pain and isolation until they comply. Vader doesn't become a good guy, but he becomes a guy with clarity about what is happening and why, and has an authentic altruistic impulse--to protect his son in multiple senses of the word--and acts on it. At the end he finds that place that Kenobi seemed to be at--not consumed by emotions that trap him within himself, but connected to the universe (mostly his son, but the universe too).
Look, you could argue that dying because of the rapid stop at the end of a long fall is some kind of Koschei the Deathless technicality where he's killed by a Jedi Knight but not "struck down" by anything but physics and deck plating and therefore can't metempsychosis himself into someone, but really I think the point is...Palpatine's death is undignified and that's perfect. This is also an inversion of Kenobi's death: Palpatine can't let go, has no actual legacy, and is incapable of perceiving the world outside of his appetites; his actual conduct in the face of death directly contradicts his earlier "as planned" smack talk. He's thrown over a rail so surprised by the assault that he actually grouses about it like an upset old dude rather than a Sith Lord. He sprays Force lightning in a kind of incontinent way and has no fall back tricks to use against Vader or save himself from the fall with telekinesis or whatever. If you divide 1 by the ending of Scarface, you get this death scene.
Sic semper creepy uncles.
Bless Ian McDarmid, but they never should have brought him back for the sequels.