I count it success. The CNC cut plywood, sanded with 320 grit sandpaper (to remove traces of burning):

It looks nice. The living hinges are half success. Basically OK, but not enough lines. I have put them on 5mm from each other, and it looks like too much. I will try out the 3mm.

There are cracks, and I hope that with more lines it will bend fine. We'll see soon.