To what extent is the circulating story true regarding the events of the Battles of Jamal and Siffin, including the reasons for the disagreement among the Companions, the role of the Saba'iyyah in igniting the fitna, and the positions of Imam Ali, Aisha, Talha, Zubayr, and Mu'awiya?

What is mentioned in the question is a summary of what is reported in the books of Sirah (biography) and history concerning the Battles of Jamal and Siffin. It is advisable to avoid delving into these tribulations that occurred among the Companions, and to believe that they stemmed from ijtihad (independent reasoning), and that both the one who erred and the one who was correct will be rewarded. One should adhere to the saying of Omar ibn Abd al-Aziz: "That was a tribulation from which Allah protected our swords, so let us protect our tongues from it."