I think that The New Mutants film could take place in the Logan timeline. One of the first reasons I came to this conclusion was footage from Logan of the young Mutants at Alkali-Transigen was used in the film. It's possible that while Alkali-Transigen for the most part suppressed the X-Gene, they were only about 99% successful, and only a small number of Mutants could be born outside of their control. This would explain Dani not knowing much about Mutants beforehand. Also, it has long been speculated that Alkali-Transigen is a subsidiary of the Essex Corporation, Essex and the Logan footage in the film link the two organizations.