So the CT novel isn't actually a straight adaptation of CT? Then... what does it tell? Can you sum it up?
The second CT novel is an adaptation of CT, but the first one isn’t. It focuses on Tsubaki in a timeline where Noel doesn’t exist - this is very likely the timeline that Hakumen comes from, as well.
Basically, Tsubaki runs around trying to find Jin as Hazama manipulates her from the shadows. Ragna is basically doing the same thing he does in CT, except he kills Arakune (with Tao watching) because Litchi was treating Tsubaki’s injuries after she got into a fight with Tager and lost. Tsubaki runs out of the clinic, leaves her handgun behind (yeah, she doesn’t use Izayoi here).
Terumi gets into the Alucard Castle, taunts Rachel, then leaves. Ragna fights Carl outside the NOL headquarters. Ragna gets in, it’s basically the same as CT. Ragna and Nu fight, Jin interrupts and Nu goes to kill him, but Tsubaki jumps in front and dies protecting him. Nu and Ragna go into the cauldron, and Jin jumps after them.