Who has to indicate in this situation?

You were right: you and the blue car must indicate.

In Germany you must use the turn signal whenever you change direction, and that also includes “following the bend” of a priority road at an intersection. Here, the priority road does not go straight ahead; it bends left (shown by the additional sign under the priority-road sign). So if you (and the blue car) want to stay on the priority road, you are actually turning left and must signal left to make your intention clear to other road users.

The red car does not have to indicate in this situation because it is driving straight along its road (it is not turning into another road). Rule of thumb: signal for any turn or lane change; if the priority road bends and you follow it, you still signal in the direction of the bend.