Agreed.
From a technical standpoint, this also makes no sense. Someone with paranormal abilities of not requiring nutrition and being unable to eat food shouldn't receive a diagnosis of anorexia nervosa, it becomes meaningless. It's like saying that someone who spontaneously combusts if they leave their house has agoraphobia. This person could have food phobia, or some kind of unspecified eating disorder, but applying an eating disorder label to someone who cannot eat is just silly.
Having said that, this is not really that different from a real person with anorexia, which is not a good thing in this case. The Foundation probably wouldn't bother with a case like this - while theoretically impossible, there are enough True Weird Medical Stories (You Won't Believe #3!) involving someone who never ate any food but survived for many years that the Foundation would ignore them.
More importantly, the author has presumably wanted to write something about mental illness and eating disorder, but it's not using the genre well. The Broken Masquerade stuff does this by drawing an allegory between mental illness and the difference/othering of having other various anomalies/superpowers/whatever (see Confiscated Documents March 2022 etc). This, however, is just… someone with mental illness with some Foundation setting window dressing. If there are no meaningful sci-fi/paranormal components, you would be better off reading/writing about actual real people with mental illness, particularly given the superficial nature of this character. -1
