Gosh, that was an 1GB git clone just to have a quick peek inside a KiCad project.
This project looks very much like it was made in some other program first, and then converted to KiCad. That whole table (On the F.Dimensions layer) is made from individual text strings and graphics lines.
KiCad does have: PCB Editor / Place / Add Stackup Table but it is only a table with text. It does not have the PCB cross section drawing. I also do not know whether this can be placed via a script. Doing this would need a way to set the layer and coordinates too.