We usually use the style:

if (inverted)
  animation = new Tween<double>(begin: 1.0, end: 0.0).animate(animation);

(rather than ?:)

Done.

Maybe mention in the comment that the reason we want to do this is to update the logic that depends on _isTransitioning in the build method.

Done.

remove "right" in the comment?

Done.

don't use strings if you can help it (since keys are compared). A ValueKey<CrossFadeState> would probably do the job more efficiently. (At least, I hope that comparing an enum is faster than comparing a string...)

Done.

you want to exclude the one that's going away and include the one that's coming in, regardless of the state of the animation.

Ah, good catch! Done.