Nick Petit

Use the RBD Connected Faces SOP before deleting geometry, and make sure you enable the Face Name Attribute.
Delete your pieces and chips, then use the RBD Disconnected Faces SOP to remove connected faces. Make sure you enable the Face Name Attribute on that node too.
When using the primitive attribute to store the connected faces, it may not cover ALL connected pieces - with more complex fractures a face could be connected to multiple pieces. Using the Vertex mode instead of Prim mode will store all the connected faces at each vertex instead of 1 per prim. It's normally is enough to avoid unwanted holes around the corners of pieces at the intersection of multiple cutters.

Here's an example hip file.

If you are using the Background Plate LOP, make sure you have geometry to project the plate onto, and then make sure your object is refractive. In Karma CPU this should just work.

in a point wrangle with the rbds in the first input and the constraints in the second, this will give you the number of constraints connected to each piece.