Although Palpatine told Dooku the plan was for Obi-Wan's death to be used as leverage to turn Anakin, this was not the case at all. Sidious wanted Anakin to kill Dooku. The killing of a powerful Sith such as Dooku was the tipping point to set Anakin on track to the dark side.
The most likely explanation is that Dooku hid his precious dark side artifacts from Palpatine himself. The Emperor possessed a treasure trove of such relics, and it's reasonable to assume the Empire's raid on Serenno was all about ensuring none were left behind on Dooku's homeworld.
In 20 BBY, bounty hunter Moralo Eval, at the time under the employment of Confederacy of Independent Systems Head of State and Sith Lord Count Dooku came up with a plan to kidnap Supreme Chancellor Sheev Palpatine to strike a decisive blow against the Galactic Republic.
Dooku played his role perfectly, splitting the galaxy in two and creating the perfect crisis for Palpatine to erode the Republic's democracy until it functionally became the Empire. As revealed in Star Wars: The Secrets of the Sith, Dooku's death was always planned.
Once a Jedi -- trained by Yoda -- he became disillusioned with the Jedi Order and thirsted for greater power. Dooku voluntarily left the light side behind and became Darth Sidious' dark side disciple, taking the secret name Darth Tyranus and leading the Separatist army.
Why Didn't Count Dooku Expose Palpatine in Revenge of the Sith? Star Wars Explained
Why didn't Dooku overthrow Palpatine?
With how different Dooku was from the other Sith, there was a part of him that didn't even want to dethrone Palpatine. He truly believed that the Republic and Jedi were useless and saw the Separatist Army as something necessary to gain freedom for the galaxy.
Count Dooku Truly Wanted To Overthrow Palpatine With Obi-Wan
Even before Obi-Wan discovered that Dooku had fallen to the dark side, he refused out of loyalty to the Republic and distaste for the Separatists' oppressive leadership.
Yoda had to shoulder that decision for years. However, he ultimately understood the importance of life, and the power he could have used to defeat Dooku would have been much better used to preserve two lives. Over the years, Dooku would commit countless atrocities and also suffer incredibly embarrassing defeats.
Indeed he did. Dooku (aka Darth Tyrannus) knew his master's identity. At this point the Jedi thought Dooku was the Sith Master. The kidnapping was planned to reinforce public support for Palpatine while further confusing the Jedi about his true identity.
Coruscant is the political hub of the galaxy that consistently holds those of great power and influence, both politically and through the Force. For this reason, it's never been openly attacked during wartime.
While Dooku may be powerful enough to hide his Sith eyes, there is another reason for his unusual appearance. Dooku's eyes were never yellow because he did not have the same motivation and emotions as other Sith. Dooku was an idealist who left the Jedi because he thought they had lost their way.
With Anakin's mother dead, his padawan Ahsoka estranged and his faith in Obi-Wan and the rest of the Jedi council fading, Padmé was all he had left by the climax of Revenge of the Sith. By eliminating her, Palpatine would be the only one left for Anakin to turn to and therefore would have complete control over him.
He also knew that Anakin had been corrupted by the dark side of the Force, and he wanted to spare him from any further suffering or guilt. By not saying anything when Anakin was about to execute him, Count Dooku showed mercy towards his former apprentice and allowed himself to pass away with dignity.
Sidious may have given Dooku the title of Darth Tyranus, but because the Jedi Order knew him as Count Dooku, greatly preferring to not indulge his role as a Sith, they continued to call him by that name.
Dooku argued that having a well-respected Jedi such as Obi-Wan on their side would bring legitimacy to their cause, and wash away any doubts the integrity of this New Order.
Dooku belonged to the aristocracy, and his weapon reflected an older, more chivalric style than the Jedi he faced. It also reflected his status as the head of the Separatists: the lightsaber looked far more ceremonial than practical, suggesting that he himself did not face combat nearly as much as the Jedi did.
In the Star Wars prequel trilogy, the Jedi Order learned that Count Dooku was a Sith Lord in the film "Star Wars: Episode II - Attack of the Clones." The revelation occurred during the course of the movie's events, which were set approximately ten years after the events of "Star Wars: Episode I - The Phantom Menace."
