Hello Torsin,
how nice that you have turned to Wefugees with your question.
You have a residence permit according to § 19d. You get this if you do a qualified training. If you continue to work in this profession after completing your training, your residence permit will be extended for another 2 years. This means that for a maximum of 5 years your residence title depends on you working in your learned profession.
This residence permit can be revoked by the Foreigners' Registration Office if the employment relationship is terminated, e.g. through your fault, and you cannot find a new job in your learned profession. Another reason for revocation would be if you have committed a criminal offence.
What this means for you is that if you clarify with your current employer that they have no objection to a mini-job, you can accept it. This will not change the conditions of your stay. Your employer might object if the mini-job affects your working hours in your full-time job. Therefore, your employer must agree to it so that there are no misunderstandings or irritations later on.
I wish you all the best.
Best regards
Gabriele