Combine simple syrup and xanthan gum in a small bowl, whisking thoroughly until smooth. Transfer this mixture into a blender. Incorporate the instant coffee packet, followed by the milk, caramel syrup, and granulated sugar. Add the ice and blend the contents until a creamy consistency is achieved. Generously drizzle caramel sauce along the interior sides and base of your serving cup. Pour the blended frappuccino into the prepared cup. Crown with a swirl of whipped cream and finish with an additional drizzle of caramel sauce.