I think this should be solved, negociated,.. between your own car insurrance and the other party,
unless you receive directly the cash?
My car get repaired and the body shop was constantly sending new quotes, especially after removing parts.
So not only the bumper assembly needed to be replaced, but finaly also the whole rear panel.
Also when replacing the rear quarter panel, the roof glass has to be removed.
And even after taking multiple precautions, the roof glass broke and had to be replaced.
Also, make it clear about the car rental coverage, the insurance might only want to cover 30 days
while you car might be not available for months, especially if the car is not drivable, or cannot be locked
and should be parked inside a garage or given to the body shop until it get repaired.
Considere contacting a Diminished Value appraisal for additional payment.
If you get any injury, hire a lawyer.