Thank you for your reply! Tried several more options.
I realized that I can't use setTimeout here, because it affects the performance of Barba JS a lot. I took it and the header started working normally, the class is added after the barba transition, but now a new problem has appeared, which is directly related to the ScrollTriger. The END marker of the white section should be at the very end, but for some reason it is placed in the middle. How to set the delay, I don't know, because again, it is not desirable to use setTimeout.