as far as I know it is not possible. STEP file can include information about geometry and colour, not the texture.
what is the intended end use of the file? Why does it need to be STEP?
Your file size will be proportional to the detail of the 3D surface. From your image it looks to be subtle but complex as the surface is very textured.
What software do you have access to? SolidWorks probably isn't the best suited for this type of task. If you have acces sto 3D Studio Max that might be better. Or you can use Blender which is free, both will require some learning if you've not used them before. Again, this is dependant on what your end goal is.
Intended end use, is to use it in SolidEdge or SolidWorks Assemblies. With .step I can handle always the files in aforementioned programs.
Someone access and time, to see of 3D Studio Max can import in .ply and export it in .step?