In the middle of a reread after reaching Chapter 62 and this chapter stood out to me:
Kate said "The doll will end up looking like the complete existence." I don't know if that's because of the different translation team, but I think she's referencing the fact that living dolls and shadows are supposed to emerge. Which REALLY makes me wonder how much she knows and how she found out all this stuff!!
@fennec yeah in the middle of re-reads too you can notice a lot of things about the characters.
earlier chapters also shows Kate noticing Clingers existing (leftover soot moving) and stepping on it. Then afterwards she makes SootMan (like a small snowman made of soot). It shows that she is quite a curious one and that's how she knows about a lot of things and shadow's house secrets etc. She was obviously testing out if Soot can move when they're in certain shapes. During that chapter too after Emilyko reveals she was watching her making Sootmen, and. Kate says "constantly being watched makes me feel uncomfortable" which matches with what Edward said regarding Kate's report i think. About it being "too clean / suspiciously as if Kate is aware she's being monitored".