If the perspective and displayed mesh don’t change then the easiest would be creating this texture in a vector drawing program like Inkscape, Illustrator or Affinity Designer.
If you want to look at the mesh from any angle then you can use textures to put the lines on the mesh. From a distance it might be alright but it is possible that it will look like what it is: lines painted on a surface. You can fake some thickness by adding shells, multiple layers to each surface.
The most reliable solution would be actual tubes for the lines. Houdini has tools for such a task but it should be trivial to do in other 3D apps as well. The downside is the increased polycount and that the tubes will consist of tiny triangles which are not GPU friendly.
If you can live with a fixed screen space width then you can generate a thin quad strip instead of an actual tube and assign a wireframe material to it.