While you are still in the asylum process, you are not obliged to obtain a passport. The fact that you have contacted your embassy can have a negative impact on your asylum application. A question from my side would be why you are attempting to obtain a passport while in the asylum process?
We cannot provide legal advice here and so I cannot say if withdrawing your asylum application in order to receive an Ausbildungsduldung would be the correct decision. My question here would be what benefit you would have from changing your status from Aufenthaltsgestattung to Ausbildungsduldung? As long as your case is still undecided, you may still end up having your asylum application accepted and receiving a residence permit, with which you can continue your Ausbildung and work. An Ausbildungsduldung is not a residence permit. It is the lesser status of Duldung with some protection against deportation while you are doing the Ausbildung. If anything would happen during the Ausbildung (health problems, issues with the company etc.) then oyu lose this status unless you find a new Ausbildung.