No, you'd get out, realize what was happening, and get back in the car and put it in neutral or otherwise gently move it 6" to stop crushing the person.

Aren’t you not meant to do that until paramedics arrive in case the removal of pressure from the injuries makes the situation worse?

I think in a scenario where this just happened you'd want to remove the pressure immediately. The pressure is going to lead to lower or no blood flow to the limb, which will greatly increase the chance of losing it.

The article mentions that police asked them to leave the car in place until the FD arrived.

They had to drive the car remotely, right? That wouldn't have 10% of the finesse of a human in the front seat with a hydraulic brake pedal. But I wasn't there so just speculation.

What surprises me is that people didn't lift the car off her. 3-4 adults should be able to lift even an EV a few inches.

Just removing the object crushing a person could result in their death. You need medical professionals on hand to ensure that removing the object doesn't lead to untreated issues.