My car shuts off when I turn the steering wheel

Almost has to be a short around either the steering shaft inside the car or outside under the hood. If it is a repeatable item it should not be that hard to find. But there is a lot of wiring in that car. Does it do it regardless of which direction you turn? If you hold the wheel in the same spot after it shuts off does it restart, or do you need to move the wheel?

Okay if it does it both ways that makes it a bit harder. If it only acted up one direction you would look for a wire that only moved when you turned that way. That you have to center it back up for it to start sounds like it is more than likely an actual connector and not a loose wire. Either direction stresses the connector. When turned straight the connector relaxes and power can flow.
If you put the transmission in reverse, stand on the brake and give it some gas does it shut down? How about in drive? Another thing you can do is gently pull on the wiring harness connections and see if you can trigger the problem. Have someone slowly turn the wheel back/forth as you watch the wiring. Stuff that doesn't move is not the problem.

If you have access to a factory level scan tool you could watch the engine control system voltages as you turned the wheel.

Transmission wouldn't cause that. It's something in the wiring but finding it will be the trick. I would start by picking one area, with the engine running tug on the harness in the areas around the steering. The reason it's tough to find is that there are hundreds of wires and you may have 1 or 2 causing this. The only good thing is you know it has to be somewhere near the steering parts.

If it only does it turning left, look at wiring that moves only while turning left. Turn the wheel slowly left and when the engine stops, look close at any connectors that flexes or get pulled. Then start slowly moving those harnesses until you find the one that shuts down the engine. Good luck with it.

It could be the harness to it, but without proving it I would keep looking. Easy add-on test. Grab a section of harness, hold it tight and have someone turn the wheel. If the wires can't move they shouldn't shut off the engine.

Wiring can be a bear to sort out because modern vehicles have so much of it. Shorts and intermittent faults are hated items.

The harness that is likely causing your problem starts under the hood.
Here's hoping you get it sorted out.

Good Luck and you are welcome.

If the mount is letting the engine shift that far it could pull on the wiring and shut it down. It's not real common but it does happen. Easy for you to verify, Watch what the engine does if you have someone hold the brake down with the car in drive and step on the gas, then switch to reverse and repeat, the engine shouldn't move much more than an inch or so either way.

Just checking to see if you got the problem solved? If you did what was the issue? Broken mount chaffing the wiring?