Is it obligatory to pay the mechanic the agreed-upon amount after repairing the car, given that what he did was unlawful, and what should I do regarding the company?

What you did was cheating and betrayal. The Prophet, peace and blessings be upon him, said: "Whoever cheats is not one of us." This mechanic does not deserve payment for his unlawful work. You are required to repent to Allah and to give the agency that sponsored your car the equivalent of what they repaired. You must also guide the mechanic to sincere repentance.