no the Yoda lightsaber fight in Episode 2, what did it add to the story
Dooku was Yoda's last padawan learner. Up until that moment, he was just a member of the Lost 20 (Jedi who left the order) and not thought of as a Sith.
Deleted Lost Twenty scene.
He was still respected in the Jedi Order even though he was a Separatist prior to the Battle of Geonosis. To the Jedi, the only known reemerged Sith (Maul) was thought to have been killed on Naboo a decade earlier. The fight solidified Dooku's break from the Jedi Order and the bond between master and former apprentice was forever broken.
From the AotC novelization (Mace talking to Yoda about Padme's accusation of Dooku) :
“It troubles me to hear Count Dooku’s name mentioned in such a manner, Master,” Mace said to Yoda as the Jedi made their way back to their Council chamber. “And from one as esteemed as Senator Amidala. Any mistrust of Jedi, or even former Jedi, in times such as these can be disastrous.”
“Deny Dooku’s involvement in the separatist movement, we cannot,” Yoda reminded him.
“Nor can we deny that he began in that movement because of ideals,” Mace argued. “He was once our friend—that we must not forget—and to hear him slandered and named as an assassin—“
“Not named,” Yoda said. “But darkness there is, about us all, and in that darkness, nothing is what it seems.”
“But it makes little sense to me that Count Dooku would make an attempt on the life of Senator Amidala, when she is the one most adamantly opposed to the creation of an army. Would the separatists not wish Amidala well in her endeavors? Would they not believe that she is, however unintentionally, an ally to their cause? Or are we really to believe that they want war with the Republic?”
Yoda leaned heavily on his cane, seeming very weary, and his huge eyes slowly closed. “More is here than we can know,” he said very quietly. “Clouded is the Force. Troubling it is.”
Mace dismissed his forthcoming reflexive response, a further defense of his old friend Dooku. Count Dooku had been among the most accomplished of the Jedi Masters, respected among the Council, a student of the older and, some would say, more profound Jedi philosophies and styles, including an arcane lightsaber fighting style that was more front and back, thrust and riposte, than the typical circular movements currently employed by most of the Jedi. What a blow it had been to the Jedi Order, and to Mace Windu, when Dooku had walked away from them, and for many of the same reasons the separatists were now trying to walk away: the perception that the Republic had grown too ponderous and unresponsive to the needs of the individual, even of individual systems.
It was no less troubling to Mace Windu concerning Dooku, as it was, no doubt, to Amidala and Palpatine concerning the separatists, that some of the arguments against the Republic were not without merit.