as far as I understood, coz it was confusing me too, the original beatrice did die and reincarnated(??) into her korean self. that explains why in the later chapter when they meet the master/i forgot what the webtoon calls that person, and it flashes back to modern day korea with her speaking to that person and promising to help if she gets into uni, the master person pushes her and says "beatrice" after she gets into uni.
i know this whole reincarnation into the real world from book and back doesn't make sense, but it's part of this whole otome isekai genre thingy so i just kinda roll with it.

I just want to know what happened to the original soul of beatrice. If there are three souls involved in the switching. Did beatrice die? I seem to skip or haven't thoroughly read the specific chapter detailing the black magic part.