Welcome back to the Wefugees Community and thank you for reaching out to us again.
Unfortunately, I am not able to predict the time the immigration office will need to issue your residence permit. You are right, holding a residence permit according to section 25 (3) of the German Residence Act (with a national deportation ban), you are entitled to receive social assistance from the Jobcenter. However, I would recommend you to get in touch with the Jobcenter yourself and apply for the so-called "Arbeitslosengeld 2" in case you can not cover your life expenses. This is nothing happening automatically. They will also ask for your bank statements of the past three months, your renting contract of your flat etc. Only if you submitted all the required documents they will pay the money.
In case you are facing problems due to the processing time of your residence permit, you may contact a migration counselling office for support. They can help you to ensure a smooth transition from the "Sozialamt" to the "Jobcenter".
I hope this helps and all the best,