Newb help - looking for the appropriate software and/or workflow

I'm dabbling in 3D modeling to allow for fast iterations on templates for 3D stained glass pieces. I'd need to divide my model into 2 halves to allow for a mirrored design, draw lines over the surface of the piece to break it into segments using both perfectly straight and regularly curved lines, then perfectly flatten the areas between those segments. You can almost think of it as the difference between a 3D model of a swan vs an origami swan. A good example of this was done with squirtle in another reddit post here.

Does anyone have a recommended software and/or workflow to allow me to do this? I've dabbled in a few different programs but none seem to have all of the abilities I need. It would help if it's user friendly but I'm happy to put in the hours to learn my workflows.

Thanks!