The [red] car in front of you has been driving slowly for some time now. What is the correct course of action in this situation?

You answered correctly by choosing to maintain your speed behind the slower red car. According to German traffic rules, you should only overtake when it is safe and legal to do so. Just because the road looks clear does not automatically mean you may overtake. You must ensure there are no traffic signs prohibiting overtaking, no oncoming traffic, and that visibility and road conditions allow a safe maneuver.

Closing the distance and sounding your horn to pressure the driver is not allowed and can be considered aggressive or dangerous driving.

Maintaining a safe distance and your speed helps prevent accidents and ensures you can react to unexpected situations. This cautious approach aligns with the concept of defensive driving, especially on rural roads where conditions might change suddenly. In summary, wait for a clearly safe and permitted opportunity to overtake rather than reacting impatiently.