There’s a local article about this here: https://www.rnz.co.nz/news/political/564504/melatonin-to-be-sold-over-the-counter-psilocybin-to-be-prescribed

A part I found interesting:

Associate Health Minister David Seymour announced the decisions on Wednesday afternoon, noting they were made by MedSafe rather than politicians.

“Certainly I’ve discussed with some of them … some of them were very enthusiastic about the melatonin but ultimately they respect that it’s a technical decision for MedSafe.”

So this was not 'legalising"or any law change, but instead or medicine safety department has determined there are proven health benefits, risks are well understood and deemed to be lower than the benefits, and there is a quality supply. I suspect other countries like Australia doing the same have allowed a pharmaceutical source of psilocybin to establish and so made this decision easier.