thank you for sharing your question with the wefugee community,
What you have been told by Ausländeramt is correct:
After you handed in your papers and they have checked the documents and done the necessary backgroundchecks they order the Aufenthaltstitel from the federal printing agency (Bundesdruckerei) in Berlin which might take a few weeks.
I hope my answers were helpful and I would 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 and get confidential individual advice in a secure virtual space without other people reading our conversation. Further information: www.mbeon.de.