Well, if you're having your insurance cover it, you just have to tell the adjuster and the shop that you want OEM only, as least in NYS that is your right. They'll try for aftermarket or the used, seconds parts. In either way, unless you're paying for it, the shop is going to be replacing that bumper, fender, quarter panel maybe, the hood perhaps and will either paint it all themselves with a blending or send it to another shop to paint it for them.
The shop will take it apart and check for any other damages and repairs needed, come up with the costs and paint needed, plus the time to repair. Again, if you have collision, your insurance will pay this, minus your deductible, but the shops usually work with you on the deductible from you.
As for the HUD pop-up, the person that cut you off, without knowing the full extent of what happened, was probably just out of view of the camera and was too sudden. A lot of stories you hear online that AEB systems that use cameras, the blind spots are the corners of the vehicle, not enough time to register a vehicle or object and stop the car.