Summary
Ahsoka Tano believed Anakin Skywalker was dead after Order 66 because she couldn't sense his presence in the Force anymore.
Ahsoka had witnessed Anakin's flirtation with the dark side in the past, but never imagined he would ultimately betray everyone.
It was only when Anakin fully embraced his alter ego, Darth Vader, by surrendering himself to Palpatine, that Ahsoka had to confront the harsh reality of his transformation and see him with her own eyes as Vader.
Star Wars: The Clone Wars showrunner Dave Filoni has clarified why Ahsoka Tano believed Anakin Skywalker was deceased following Order 66. During the unfolding events of the Siege of Mandalore arc, Ahsoka experiences a profound connection to Anakin through the Force, sensing his agony as he rescues Palpatine and succumbs to the dark side. Although she remains unaware of the exact events that took place on Coruscant, Ahsoka strongly intuits that something dreadful has befallen her friend.
In a 2016 interview with Star Wars, Filoni divulged that Ahsoka's ability to perceive Anakin's presence in the Force diminished considerably after Order 66.
George Lucas and I discussed this aspect. After the execution of Order 66, Ahsoka survives and has a moment where she reaches out to the Force in search of Anakin. Regardless of her location in the galaxy, she can still sense his presence. It's important to note that she cannot pinpoint his exact location like a metal detector, but she can feel a reassuring presence indicating that her friend is safe and alive. However, when Ahsoka reaches out after Order 66, she no longer senses Anakin's presence. It has vanished, leading her to believe that he has perished.
In the final version of the Siege of Mandalore, the events unfold differently, but the absence of Anakin's presence in the Force remains unchanged. There is a perspective that suggests Anakin's transformation into Darth Vader occurred at various points during Star Wars: Episode III - Revenge of the Sith. Nonetheless, according to Filoni, the moment when Anakin offers himself to Palpatine symbolizes the definitive shift.
Did Ahsoka Consider Anakin's Turn To The Dark Side?
Considering how powerful Anakin was, one would assume that Ahsoka would have considered the possibility of his survival after Order 66. Having witnessed Anakin's flirtation with the dark side during his time as her student, Ahsoka would have found the events in Palpatine's office eerily familiar. Although Ahsoka couldn't comprehend the idea of the honorable person she knew betraying everyone, she still had to entertain the thought.
In a sense, Ahsoka's interpretation was accurate. As Obi-Wan stated and Filoni suggests, Anakin ceased to exist when he embraced the Sith and transformed into Darth Vader. Among the countless Jedi who were brutally eradicated during Order 66, the downfall of Anakin Skywalker is perhaps the most tragic. It wasn't until Ahsoka personally saw Anakin's presence beneath Vader's helmet and heard his voice that she finally came to grips with the extent of his transformation, a realization that haunted her for years until she could accept that his essence had been redeemed.
Source: Star Wars