This gets cited here weekly, usually second-hand, so it is worth setting out what it does and does not establish.
The mental-health dimension is under-measured in the trial literature and the reports here are consistent enough to take seriously. On the positive side: reduced anxiety around food, better self-image, more confidence. On the difficult side: grief for the years lost, identity disruption, relationships built around eating, and the loss of food as a coping mechanism with nothing put in its place. Rarer but real: anhedonia and emotional flatness. Regulators have started asking for validated patient-reported outcomes in this class; the existing data gap is not evidence of absence.
Where I think it is weakest: the follow-up is short relative to how long people actually take these drugs, so durability is an assumption here rather than a finding.
So the question, as narrowly as I can put it: how people separated a drug effect from the ordinary consequences of a large deficit and disrupted sleep, because I cannot. I have searched first, so if this is covered somewhere point me at it and I will read it.
Note on sourcing:
Figures above are from the primary publication rather than the press summary. If a number here disagrees with one you have, post yours and we will work out which of us is reading a secondary source.