Berlin definitely has some.

>but I don't think there's a single one of those large LED screens (like the ones on time square) in Hamburg

yes, I also did not notice any of those here in Hamburg. there is a smaller one in Harvestehude; even those are so rare that I clearly noticed this one.

In very rural southern Germany, I know several electronics stores who have 7x4-meter panels, and I know a spot where they are mounted to a mast next to a federal road (with farmland around it). People always think "Times Square", but ultimately, the problem is bigger for the displays are smaller.