Unwrapping and Flattening... my hopes and dreams

I tried another method, using Blender. I unwrapped (all at once) the model (seams for each edge) and exported UV Layout as SVG. In Inskape I saved as DXF and then imported into SketchUp.

Depending on the need, instead of each edge being a seam, a route of those seams can be created and the faces can be connected. But this is to be tested.

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The solution offered by Pierre is probably the right one, being a specialized software for that and having the automatic unfold option. In Blender it is necessary to select which edges to separate.