Darth Vader's betrayal in Return of the Jedi was no surprise to Sidious. The Emperor had believed his apprentice was going to betray him, although he seems to have expected it to be in the traditional manner of the Sith rather than because he was redeemed by the love of his son. And so Palpatine had prepared for that betrayal, setting in place a Machiavellian scorched-earth scheme to ensure Darth Vader did not inherit the Empire.
As news of the Emperor's death spread across the galaxy, secret Imperial factories were ordered to begin mass-production of a new generation of droids. Within weeks, these droids had spread across the galaxy, choosing operatives to participate in a strategy called Operation Cinder. Imperial loyalists were called to launch genocidal attacks across the galaxy, Palpatine's way of ensuring those who were truly loyal to him would be rendered even more extremist. The final battle of the Galactic Civil War was fought at the Battle of Jakku, an entire world transformed into a gigantic bomb, but fortunately one New Republic agents successfully defused. The last remnants of the Empire fled into the Unknown Regions in accordance with the Emperor's will, where they reformed into the First Order.
Alexander Freed's novel Victory's Price puts the Emperor's droids under the literal microscope, with one of them destroyed - and then taken to droidsmiths for analysis. It reveals these things wouldn't even be classed as droids by many definitions, because their programming incorporates elements that aren't traditionally part of a droid design. They actually have personalities, but these are shaped more by the dark side of the Force than by their programming. The Emperor had evidently learned how to blend artificial technology and the dark side, a remarkable feat that may well have only been made possible by his observations of Darth Vader.
These so-called "Sentinel" droids enforced the Emperor's will in his absence, and it is even possible his spirit continued to work in them from afar, given Darth Sidious was master of the dark side. If that is the case, then all the Imperial atrocities conducted after Return of the Jedi - countless acts of genocide, so many star-systems ravaged and cities destroyed - can be laid directly at Palpatine's feet. They were not merely done in response to his plans, but in accordance with his continued choices and decisions.
Ironically, Emperor Palpatine's plans went wrong. Having been resurrected at Exegol, he had intended to head off into the Unknown Regions to meet with the Imperial remnant. But the dark side corrupted the growth of the clones, and Palpatine found himself trapped on Exegol, unable to leave. That led the Emperor to create Supreme Leader Snoke to lead the First Order on his behalf, and it is possible he got the idea from having seen the success of the Sentinels.
