I don't really understand is there really an Emma path? Or it's just teasing?
Even if you reject Lucy and then after that play super cold full negative choice with Charlotte, you still "end" up with her
:thonking:
There isn't a "default" Charlotte LI route/path; the only way you get on her path is picking the one choice at the scene where it says to start her path. If you don't take that choice, which is clearly labeled if I recall correctly, then you won't be on her path. If you want a save for the Suzi path, once it becomes available, you'll have to turn down Charlotte, Lucy, and Suzi, in order to get it. Since their paths are mutually exclusive.
And yes, Emma has just the start of an actual Path you can start. It's not very developed yet, as Emma has had to break out of her naivety bubble. Now that that started to happen after she was attacked, which has started to occur. She also needs to sort out the confusing dreams/feelings she's had about the MC.