It really feels like if senpai could clear this up if she was more overt in saying that she liked tsumugi before the string showed up, not because of it.
It really does seem that’s mostly what’s stopping her from accepting
The thing it that the senpai didn't realized her feelings before being binded by the string. She sure had feelings, but I don't think she was aware of them. The string allowed her to realized her feelings, but I'm not sure she understands that she was already in love before that.
The plot is pretty thin so far. I like the characters, but the MC is a bit too stubborn. Sure, admitting that love cannot exists outside of the bond would be admitting that she should have never been born in the first place. But it doesn't mean that binded love is not true as well. Both can be true as the same time.. her stubbornness regarding that sounds just like a plot device to drag their story longer...