Family reunion visa to join blue card holder

As you encounter right now, Geman officialdom is generally slow, inefficient and opaque in their working.

And local Foreigner Authorities ("Ausländeramt") are among the worst here.

But since you depend on them, there isn't much you can do but wait.

In principle, you are entitled to a result of any official process within three months (by law) - unless reasons outside of the authority's influence prevent this. You could even sue them, but in reality this seldom helps:

• Courts are also slow and inefficient,so a decision might not be reached before the original application is processed anyway.
• If you win, the court gives the authority another timeframe to process your request (typically a month).If they ignore this, you'd have to sue again. You are not entitled to any damagesor compensation.
• If you lose (e.g. because the authority claims a reason beyond thei control),you have to bear the court fees.
• It is unclear, in your case, which authority to sue: The embassy (where you submitted the application, but which cannot control the Foreigner Authority) or the Foreigner Authority (which you did not directly ask to do anything).

My advice: You won't be alone in waiting six months or longer. If you have time and energy to spare, call them daily!

I agree with Beppi. One would expect 3 months to be enough time but many things are still delayed, if happening at all, due to Covid. Most safety measures have been lifted but there is an acute shortage of workers in many jobs including government ones. 

I can also imagine that due to the instability in Iraq in recent years that all people coming from there are closely scrutinized and doing so might be extra complicated. Don't give up. I would not pester officials on a weekly basis but maybe once a month inquiring about the status of the application would seem appropriate.