Dear @Freetown,
Welcome to the Wefugees Community and thank you for reaching out to us.
First of all, congratulations to your completed "Ausbildung" - this is a very big and important step!
Regarding the situation described, I can totally comprehend your struggle and your need back then to furnish your apartment. But as far as I understand, you did not inform the "Sozialamt" about the Berufsausbildungsbeihilfe (BAB) which you received as an additional allowance. This would have been necessary as the Sozialamt then would have been recalculating your income and subsequently your needs. Asylum seeker benefits are paid out on a subordinate basis. Unfortunately, regardless whether it's "Bürgergeld" or asylum seeker benefits, the social money will always take into account any income of an applicant (and adjust the social money accordingly).
Maybe you can approach it this way, in an emergency situation you were able to set up a home for yourself. Now you earn money and can pay it back like a loan. This does not mean that I encourage cheating the authorities (as this can have severe consequences). However, as you did not know about your obligations, I would just try to sort it out as quickly as possible. You may ask a counselling office for support in the negotiations i.e. in terms of an installment agreement. They can also check with you if the demands/the sum is actually correct.
In any case, please don't hesitate to get back to us with any further questions.
All the best,
Meike