Say what you will about ol’ Palpatine, but nobody can deny he’s a master manipulator. Throughout the Star Wars prequel trilogy, we saw him play a long game of galactic chess, using the Clone Wars to put the Jedi Order in an unwinnable position, engineering a situation where he was made Emperor.
That scary level of perception was on display in the last moments of Obi-Wan Kenobi, too, when Palpatine video-called a gloomy Vader to tell him to knock it off with the whole Obi-Wan obsession and keep his eye on the prize.
Fans on r/Star Wars have noted that Palpatine correctly identifies that any reminder of his life as Anakin severely weakens Vader’s effectiveness. In fights with Obi-Wan, Luke, and Ahsoka he’s reminded of his past, and becomes more vulnerable (with Luke sensing this conflict inside him). However, in the fight with Reva, he effortlessly wipes the floor with her as he has no personal connection.
Replies point out that this is backed up by comics and books about Vader, which show that he can sink into depression when he’s remembers Padme’s love for him. It’s also argued that the entire “Darth Vader” persona itself is just a coping mechanism to allow Anakin to pretend he’s not the same person as before, so anyone that can pierce that armor is at an advantage against him.
We already know Hayden Christensen is reprising his role once more in Ahsoka, though with nine years to go between Obi-Wan Kenobi and A New Hope, we may yet see more of Vader’s inner life while commanding the Empire.