I agree with Meike that you must contact the Ausländerbehörde in any case. But I think they won't allow you to leave germany while you're still in the asylum process. Aufenthaltsgestattung means that Germany allows you to stay for the time of your asylum case, but it does not include the right to travel/work abroad. So just ask them about the job offer, but I'm not very optimistic...
It's a very interesting question any way! Thank you for sharing it with our community!
I hope my answers were helpful and I'd be very happy if you would contact me again with further questions. I'm a consultant with mbeon and I‘ll be glad to help you over a longer period of time. Mbeon is an online advice for migrants via the mbeon app, which you can install on your smartphone for free. Download it from App Store or Google Play Store. You can find me in the mbeon app under my name “Euskirchen, Frau Schaefer” and get confidential one-to-one advice in a secure virtual space without other people reading our conversation. Further information see www.mbeon.de.