Anakin’s not gonna kill the one person who he ends up acknowledging as an evil manipulator who will at least give him what he wants. During the scene where he kills Windu has the moment is where he ends up thinking that the Jedi and the Sith are the same, only the latter is what will save his wife.
I mean Obi-Wan was also his father figure and I doubt he would approve of a Sith Lord. I’m not defending the Jedi because the order was really bad at that point and had completely lost sight of the Jedi code. But siding with a Sith Lord doesn’t seem like the right move under almost any circumstances.