I just re-read chapter one and there’s no indication Takabi is Ei-kun’s fiancée. Then in this chapter she is, but it‘s only revealed in passing.
I think Ei-kun made marriage pacts with both Takabi and Kawashima as a child but it was not made clear at all last chapter, and now suddenly Takabi...
This is like the opposite of how a mystery works. He’s already solved the crime, now he just has to wait for the killer to confirm his vision.
Although we don’t know who the dead schoolgirl is for sure, so there could be a twist there. Maybe it’s Arase in a skirt and wig, baiting the killer...