What is the correct course of action in this situation?

Because your lane does not end immediately but only in about 200 m, you should normally stay in your lane for now and only change to the right-hand lane when it actually becomes necessary and safe. Changing lanes too early can be pointless and can even create extra conflicts with other vehicles that might also want to change lanes later.

At the same time, it is allowed to pass vehicles on the right-hand lane in this situation because you are simply continuing in your lane and traffic is moving in parallel lanes. In German rules this is treated as “passing” due to different speeds in different lanes, not as a forbidden “overtaking on the right,” as long as you do not change lanes just to get past and you drive at an appropriate speed.

Rule of thumb for similar questions: If a sign announces a lane change “in X meters,” you don’t have to merge immediately; plan ahead, keep observing mirrors and blind spot, and merge when the lane actually ends. And if your lane is moving faster than the neighboring lane while you stay in your lane, that is generally permitted in city traffic and in slow/queueing traffic situations.