I strongly advise against attempting to obtain a new passport or making any contact with the embassy of your home country. Doing so weakens your case that you are need of protection in Germany and can lead to having your asylum claim rejected.
Furthermore, it is not necessary for you to have a current passport in order to work. Your ID (Ausweis) along with the written permission from the Ausländerbehörde is enough for them to employ you. Here is information from the Federal Ministry of Work about your access to the labour market (in German):
The company that wishes to employ you should fill out a form call a ‘Stellenbeschreibung’. This is not a job contract. It provides the details of the job they would like to offer you. You submit that form along with your own application for work permission (Arbeitserlaubnis) to the Ausländerbehörde. They will process it and if they agree, will write the permission on your Ausweis. The permission will only be given for a specific job with a specific company. You can then sign a work contract and begin to work.
Hope that helps, let us know if you have any other questions.