I’m sure this is possible at the VTK level and I would not be surprised if this is possible somehow in Slicer or a current Slicer extension, but I personally do not know how to find intersection points of a markups curve with a surface model. In this forum thread (Intersection two models (Plane and centerlines CT/MR) - #3 by shahrokh), I see someone has shared code for finding intersections of curves with a plane using vtkCutter, but I think this will not quite work for your purposes because it looks like vtkCutter uses an implicitly described surface (easy for a plane but maybe less so for your vessel segments). I also found this link: https://kitware.github.io/vtk-examples/site/Cxx/ImageData/IntersectLine/, which seems closer to what you are trying to do, but again may not be exactly it.
@mau_igna_06, do you have any suggestions?