[bcj]

You should be able to remove the wiring from the bent door and move it to the new door.
Yeah. A door without the sensor won't be the same. I don't have proximity sensors.

Specific sensors are all the same. The lock and unlock logic happens in the Body Control Unit.
The sensors only report what they see. Not if it matches.

There should be notation in used parts listings if there is a proximity sensor included or not.
If there isn't, find another that does.