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"Face My Fears" is the collaboration between Skrillex, Poo Bear (who produced Justin Bieber's "What Do You Mean?"), and Hikaru Utada, and will be the opening theme for the new "KINGDOM HEARTS III."
In the past, the "KINGDOM HEARTS" series had adopted remixes of the ending theme as the opening theme, so the upcoming "KINGDOM HEARTS III" will be the very first in the series to have completely different tracks created for the opening and ending themes.
The opening theme "Face My Fears" and ending theme "Chikai" will each have Japanese and English versions, which will be released as a CD single on January 18, 2019. It will be Hikaru Utada's first CD single in 11 years, since "Prisoner of Love" in May 2008.
That's not very specific and doesn't answer your question at all, but I guess that means the english and japanese versions were produced at the same time. The wikipedia article of Face my Fears says it was Poo Bear who wrote the lyrics but thats not reliable as its source references only mention that it is a collab between Utada, Skrillex and Poo Bear. Poo Bear is a songwriter so it makes sense that he wrote them, but I think it is safe to assume that the three of them contributed to the english lyrics, though maybe the japanese lyrics were written by Utada alone, unless the other two know japanese. I think it's more likely that they wrote different lyrics for the japanese version and she translated and adapted them to japanese. Its lyrics are not long and repeats a lot, it's a rather simple song that heavily relies on the instrumental part.
Maybe there's some old interview or news article on this website with more detailed info.
Edit: Here it is mentioned that Poo Bear did the finishing touches, so maybe he didn't contribute that much to the lyrics...