Used a profile gauge tool to “sample” the inside of the bowl in order to digitize a profile that I could revolve as the blank for the soap dish insert.

Scanned the profile and made it a vector in Inkscape, then exported as DXF.

Used Fusion 360 to revolve the profile and then intersected that body with a field of hexagonal tubes in order to make the final insert. There is a weird artifact that is appearing on the flat surface in Fusion360 and in the exported STL file, but this artifact didn't cause problems printing.

While printing, I became impatient and stopped the print early. I originally intented to have the print go to the bottom of the bowl, but 4-5mm of thickness was plenty and it doesn't slide around too much in the bowl.