Dear @Nevv,
thank you for sharing your question with the Wefugee Community.
If you have a new contract with different salary and different Foreigners Office (Ausländerbehörde) responsible for you, it unfortunately needs to be checked and approved again by the Foreigners Office and the employment agancy (Agentur für Arbeit).
I hope, you have got your answer. I am a MBEON consultant. If you wish to contact me directly, you can see my profile and follow the instructions there.
Best wishes
Fardeen Noori