It is rather poor that a journal like Lancet Psychiatry have allowed this through peer review.
Well, in the protocol they only said to interpret with caution. It would seem like maybe one of the peer reviewers said, "Hey, what about correcting for multiple comparisons?" So they mention it in the abstract and add a paragraph because they have to, but otherwise ignore it. However, it doesn't seem like they obeyed their own idea to interpret secondary outcomes with caution.