Menu has an initializer for this:

Menu("Geometry Editor", systemImage: "pencil.tip.crop.circle") {
    ...
}

Please use that instead.

Also, that system image is the one that Apple uses for markup, which could be confusing. Consider using a different symbol. Perhaps pencil.line? In addition, when a geometry is selected, consider updating this button's image to match the selected geometry. It is a bit confusing for the button image to stay the same, yet open different menus based on the context.

Should the systemImage remain the same to look like the menu in the Create and Edit Geometries sample?

I don't know. I wasn't aware that the same icon is used in a different sample.

Ok, I updated the systemImage to pencil.line.

Some of the properties in this extension are a single line and are only called from a single place, so there is no code being consolidated and in fact the code is more complex. I suggest inlining the body of these properties where they are called and then just getting rid of this extension.

I removed and inlined the single line non-optional properties and kept the unwrapped optional properties in this extension.