The number theory aspects here are interesting. In practice, a puzzle that slightly cheats the grid might also be interesting.
https://m.youtube.com/watch?v=f5XdPqMJVQM
I don't know if this is a specific Japanese style, but I never saw puzzle like this "in the west".
This one has a frame, but they also make some without (pieces that interlock like our puzzle), still with those weird shapes.
I really love them:)
You could probably generate the shapes automatically via something like voronoi diagram cells plus some rounding of corners?
Edit: I just realized that for kids, those knobs are easy to break off. The puzzle you showed makes more sense for kids.
If you want to go overboard, you can probably use some machine learning to decide on the curves for an arbitrary input image.