I have searched a variety of canon sources and Wookieepedia articles which might shed light on any contingency plans Palpatine may have had for the Sith Order. Palpatine does not seem to have had any contingency plans for the Sith Order upon his death, in large part because he was so confident that he would completely master the dark side of the Force and live forever.
Multiple sources attest to the fact that Palpatine thought his rule was secure and that he would gain immortality. For example:
But it was here that they would one day work together the way Sidious and Plagueis had to coax from the dark side its final secrets. In the intervening years he had actually come to appreciate Plagueis for the planner and prophet he had been. Such perilous machinations required two Sith, one to serve as bait for the dark side, the other to be the vessel. Success would grant them the power to harness the full powers of the dark side, and allow them to rule for ten thousand years.
Tarkin, p. 101
He also thought he would be able to reshape reality such that he would be immortal and omnipotent:
...he would not allow himself to be sidetracked from his goal of unlocking the secrets many of the Sith Masters before him had sought: the means to harness the powers of the dark side to reshape reality itself; in effect, to fashion a universe of his own creation. Not mere immortality of the sort Plagueis had lusted after, but influence of the ultimate sort. As his Empire swelled, bringing more and more of the outer systems into its fold, so too would his power unfurl, until every being in the galaxy was held captive in his dark embrace.
Tarkin, p. 242
One such attempt to gain immortality was Project Blackwing, which was a combination of Sith alchemy and science that ultimately failed and produced zombies instead. (In a sense, this could be considered a contingency plan to make sure the Sith Order would never be susceptible to the premature loss of its Master.)
Palpatine did know that Vader might one day challenge him and attempt to kill him. It would obviously be bad for Palpatine if Vader succeeded, but this is exactly what is supposed to happen under the Rule of Two:
Soon after destroying the Jedi, the Emperor had told Vader that he would one day be tempted to kill him. He’d said that the relationship between Sith apprentice and Master was symbiotic but in a delicate balance. An apprentice owed his Master loyalty. A Master owed his apprentice knowledge and must show only strength. But the obligations were reciprocal and contingent. Should either fail in his obligation, it was the duty of the other to destroy him.
Lords of the Sith, p. 27
Palpatine would require no contingency plan if Vader challenged and killed him because that's the natural succession from one Sith Master to the next: survival of the fittest.
The only reason Palpatine would require a contingency plan upon his death is if he was killed by someone other than his Sith apprentice. As previously mentioned, Palpatine was so confident that this wouldn't happen that he didn't really have such a plan. His confidence was warranted, too: almost no one knew he was a Sith Lord so no one would be prepared for a confrontation that had a reasonable chance to kill him. He rarely participated in battle once he became Emperor, so again he was in little danger.
The only reason Palpatine died at the Battle of Endor is that he deliberately used himself as bait to trap the Rebel fleet in a decisive battle (and either rid himself of the Jedi Luke, or gain Luke as a better Sith apprentice). Again, he was entirely confident that he would be victorious -- to the point that he was overconfident, as Luke observed:
Palpatine: I assure you we are quite safe from your friends here.
Luke: Your overconfidence is your weakness.
Star Wars: Episode VI Return of the Jedi
Palpatine had no contingency plans for the Sith Order upon his premature death because of his overconfidence in himself.
This leaves us to explain why Palpatine prepared for Operation: Cinder. As you correctly point out, the Sith Order is far more important to Palpatine than the Empire:
[Vader speaking] “For the Empire, Master.”
“The Empire?” Sidious repeated, miming surprise. “Since when do you put the needs of the Empire before our needs?”
Tarkin, p. 88
So why would Palpatine have contingency plans for the Empire but not the Sith Order? There are several possible explanations:
- It is possible for the Empire to go on without Palpatine (and thus he could devise a contingency plan for it), but the Sith Order is lost without Palpatine. As the Sith Master, Palpatine is the embodiment of the dark side of the Force and the Sith Order's power thus rests in him. If Palpatine was prematurely killed for any reason then the Sith Order would be irrevocably harmed. Even if Palpatine's Sith apprentice survived him, the fact that the apprentice had not killed Palpatine in a duel to the death would mean that the apprentice was not stronger than the master and not ready to take on the role of Sith Master. On the other hand, the Empire can go on without Palpatine -- indeed, remnants of the Empire in the form of the First Order still existed and proved to be a threat decades after Palpatine's death.
- Operation: Cinder was meant to be more of a threat than intended to be carried out. The Empire ruled through terror, and Operation: Cinder would have been only one terror weapon among many of the Empire's: Darth Vader, the Stormtrooper Corps, and of course the Death Stars. Wookieepedia's article on Palpatine notes that Queen Sosha Soruna of Naboo claimed that Palpatine left his homeworld untouched during his reign because he could torment the people of Naboo with the threat of destroying the planet's natural beauty. Operation: Cinder might have been a public threat to do just that in order to keep the populace in line and prevent anyone from even trying to assassinate him.1
(Out of universe, I think Disney screwed up and introduced a slight contradiction here. If Palpatine expected to live and rule forever and thus had no contingency plan for his beloved Sith Order, then I see no reason why he would care about a contingency plan for the Empire.)
1Arguing against this is the fact that Palpatine actually recorded a message to order the commencement of Operation: Cinder -- if Palpatine intended it to simply be a threat that he never planned to carry out, he went through a lot of trouble to prepare for actually executing the operation. Also, it's not clear that Operation: Cinder was publicized before Palpatine's death; if that's the case, then to paraphrase Dr. Strangelove: the whole point of Operation: Cinder is lost, if you keep it a secret!