Inkscape adds its own embellishments to the standard SVG format, including attributes to define layers. Add these two inkscape:
-prefixed attributes to your Processing code:
...
group.set('id', svg)
group.set('inkscape:groupmode', 'layer')
group.set('inkscape:label', svg)
...
BTW, I’m in the process of ordering an AxiDraw (A3) right now. Thanks to you, I’m learning how it works before I’ve even got my hands on it