What is correct in this situation?

Your answer is correct. This sign indicates that you are leaving the built-up area of Wilster. According to German traffic rules, the end of a built-up area is marked by the name of the town or city with a red diagonal line through it. This means that the specific traffic regulations that apply inside built-up areas, such as speed limits and pedestrian right-of-way, no longer apply once you pass this sign. Instead, the general speed limits for roads outside built-up areas become valid. The sign also shows the next destination, Schotten, 6 kilometers ahead. Understanding this sign helps you adjust your driving behavior accordingly when leaving a town or city.