A friend said Arcana would be the type to kill off Sonetto just to see what kind of expression Vertin would make. That's valid but consider this:
Arcana has an interest in Vertin. However, even if she captured Vertin, she can't make the Timekeeper obey her.
But what if they caught her puppy too? Arcana could use Sonetto's wellbeing as leverage against Vertin. Vertin would comply and help Manus with their goals to ensure Sonetto's safety. If she doesn't, Sonetto will bare the consequences. Heck, Arcana might even pull another Orange Situation since that's their favorite punishment according to Schneider (she tells Vertin that Arcana will make them kill each other when they are captured by Druvis).
If Vertin disobeys, she is the one who has to hurt Sonetto while Arcana is having way too much fun watching everything.
Personally, I find this more dramatic, angsty, and fitting for Arcana. Also, if she has Vertin, she also has leverage over Vertin's crew to some extent. Whenever things get sticky, she can remind them she owns their Timekeeper.