Dear @kariimde,
Welcome back to the Wefugees Community and thank you for your question.
As I experienced, the "Bürgeramt" (or the office at which you register) is not necessarily asking for the residence permit. You can even register without a residence permit (and have to sometimes). In case the civil servants ask for it, you may explain them (and show them) your appointment for the extension. However, in case you are obliged to live in a certain municipality or region ("Wohnsitzauflage"), you need to follow the respective rules. Also, if you receive unemployment benefits by the jobcenter, you may need to ask for a permission to move.
I hope this helps and please don't hesitate to get back to us with any further questions.
All the best,
Meike