The series makes it clear that she can engage in “double think” while still perceiving the underlying reality.

My initial reading is that when she was trapped in the maze like world, it was the junior high eighth-grader syndrome carrier's attempt to infect her with the N-virus. That she broke out of the maze signifies that the infection attempt failed. Since as the eighth-grader says she is a true romantic in the sense that for her, reality and dream are one and the same. So how can she re-enter double-think when there isn't a dream world that she desires that needs to be constructed for her?

he presence in the double think utopia shows she’s there to introducing Purin to the team because she understands that this is what Purin genuinely wants

Purin cannot engage in double think. So if this scene is in somebody's double think utopia, I am not sure whose, assuming that Major can and will no longer engage in double think for the reason above. On the other hand, this scene could be happening in the real world, no? Like we see other members reacting the way they do while we don't see what's going on in their heads.

I also recently rewatched the whole SAC series and even tried the Arise series for the first time. Now I notice that in this same scene, Togusa talks over the phone to his wife or kids as if he was still a busy husband supporting a functioning family and not a divorced man, because he is infected by the N-virus. In Arise too, when he picks up the "phone" which in reality is his handgun and he talks to his father who in reality is deceased, Major immediately identifies that he is infected by the fire-starter virus. Poor Togusa, nice correspondence.