You now want to turn right at these traffic lights with a green arrow sign. What is the right course of action?

Your answer is fully correct.

The green arrow traffic light in Germany means that you may turn right even if the main light is red, but only after you come to a complete stop at the stop line. This ensures that you have time to observe and give way to any pedestrians or other road users who might have the right of way. Stopping first and then turning only when the way is clear avoids accidents and respects traffic rules.

You must not run the turn without stopping, even if the arrow is green, because the stop line and the accompanying stop sign require a full halt. Additionally, you must make sure that your turn does not impede or endanger other road users.

So stopping at the stop line and checking that you do not obstruct others is the correct and safe procedure.