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It appears when opening the diffuse part. I've found nothing in the release notes about that. Maybe a UI bug as the "Viscosity" part is not really inside the "Diffuse" part.
With the mesh as it is in the question, no this is not possible using gn except subdividing all the mesh parts (like subdivision modifier does using "simple" option).
Well, no it was not clear: an edge is delimited by two vertices. The link you just provided has subdivision. So you need to subdivide the mesh (as you want) and set random bevel. The way it should be subdivided is to determinate, but GN won't be able to do it like in your image (as there will be horizontal subdivisions).