What is the right course of action here?

Your choice (answer 1: wait until the cyclist has completed the turn) is correct because when you turn, you must not endanger or obstruct road users who are going straight or crossing your turning path. Cyclists count just like any other traffic, and they are especially vulnerable, so the rule is applied strictly.

In this situation the cyclist is already in or about to enter the area you would drive through while turning. If you were to “take priority” and turn first, you would cut across the cyclist’s line, creating a collision risk. That’s why you wait until the cyclist has clearly finished the turn and the path is free.

Sounding the horn is not the right action here. In Germany you may only use the horn to warn of an immediate danger, not to claim priority or pressure someone to yield. The safe rule of thumb for similar questions is: if your turn crosses someone else’s path (especially a cyclist), you yield and wait rather than forcing your way through.