Accident at the time of change of track

The driver didn’t see me at the change of lane. The driver admitted the fault immediately. And she said that she would report this to the insurance company (company car). Hope she stays with me, so we didn’t call the police. (Hope that wasn’t a mistake.) Now I was at the workshop this morning because of a cost estimate and they meant I needed an expert because of the rear door. (It is slightly pressed in) I have not yet commissioned this one, since I do not yet know if the driver has reported the damage to the insurance. (They estimate the damage to approx. 2400 EUR, when replacing the rear door) Do I have to wait for the expert to go to the insurance? Or can I order it already after I know if the damage is reported to the insurance? Pictures I have in the attachment. How best to do this and for how long Can this take time? (Is my first damage)