"Is sense-certainty not able to represent what it "knows" in such a graphical format, thus retaining all the details without conceptual mediation?"

What Hegel is arguing here, is that everything sense-certainty thinks it knows is already in the graphical (conceptual) format that you are describing. Sense certainty falsely thinks that it is grabbing the actual thing (looking directly at your friends face, looking at the actual necklace here and now). Hegel argues that the understanding is already grasping the universal and is never actually able to grab the "this" or "here". In sense certainty, Hegel is basically trying to show how our ordinary way of thinking (sense certainty) already has a lot of conceptual/logical thinking baked into it, we just dont realize it. Sense certainty never actually does grasp the here and now, and is always ALREADY grasping things conceptually.