She did just clone her brain in the books as far as I’m aware.

In the show, in the Doylist sense I believe they just show it as a whole body clone because it’s an easier way to visually communicate to the audience that it’s a clone of her, as if you just saw a brain in a jar it would be less clear. For the Watsonian, I’d wager that it’s about assessing the quality of the cloning, since if you can communicate with it and it’s retained all your memories, you know the result was a success in a way she may not have been able to assess with a future-CT-scan or whatever.

Finale spoiler: Plus the whole thing at the end with her clone being deployed to cover her tracks means she may have kept the clone that would become Cortana as a full-body clone, so anyone wondering why there was a full body clone for her backup plan would understand.