Car swaying after an accident?

That requires a physical inspection. The off-center steering wheel proves there is something not in alignment. The rear of the car is steering off to one side and you have to correct for that by turning the steering wheel. Someone following you should be able to see your car "dog-tracking", meaning the car body is turned as it goes down the road.

If one of the links that holds one of the wheels in alignment is broken, it will allow that wheel to shift position as you drive. You will see that as a constant need to correct the direction the car is going. It can be very tiring to drive a car like that. In addition, the links can be bent but not broken, then when the resulting misalignment is bad enough, the car can still wander and need to be constantly corrected just from the two rear tires responding differently due to bumps in the road.

The fix for this is to identify and replace bent or broken parts, then have the car aligned. No two suspension or steering parts are ever exactly the same. That's why adjustment methods are designed in. There is an exception to this that you might keep in mind. There are three things to look at regarding the alignment, both now and after all defective parts are replaced. The first is whether the steering wheel is centered when driving straight ahead on a level road. Next is to observe if the car pulls to one side when you let go of the steering wheel. Those two things can be seen all the time. The third thing is tire wear patterns. Those take some time to show up so that is better left for the inspector or alignment specialist to "read" when determining which changes are needed during that alignment.

Start by visiting a tire and alignment shop. The people there are experts at identifying the causes of pulls, tire wear problems, and noises and vibrations. Many of them do the inspections for free or low cost. This article can provide more information on what to look for related to tire wear patterns:

https://www.2carpros.com/articles/how-car-tires-work

Beyond that, let me know if there's anything I can describe in more detail, either with parts replacement or with what effects the alignment.

I'm not convinced yet the alignment was the total solution. We know it was out of alignment by the off-center steering wheel. The fact that changed orientation from the crash damage is proof something bent to absorb the impact. Often something can be readjusted to bring a wheel back into specs, but the bent part is still there. Those alignment numbers on the computer screen only apply to a vehicle that is standing still. When you're driving, the steering and suspension parts go through arcs or other motions in a carefully-designed geometric relationship. When that changes, even though the alignment numbers look good, you can still have poor handling and / or miserable tire wear.

My recommendation is, for a first step, to return to the same shop and explain the concern. All alignments should include a final test drive where problems should have been noticed, but the specialists sees a lot of different car models and is often not very familiar with one. Offer to take him along on another test drive to point out the problem. I was the alignment specialist for ten years at a very nice family-owned Chrysler dealership. They were very good about letting me drop everything to address problems like this. This should start with another inspection, particularly on the rear, and include comparing parts on both sides to identify if something is bent. A clue will be found in any adjustment that had to be moved a lot. Doing so during the alignment usually hides, or overcomes the part that bent. At the very least, a mechanic deserves the chance to correct any mistakes. You can expect to pay for any additional parts that can be identified as being needed, but the second alignment should be at no cost to you.

If no solution can be found, visit a second tire and alignment shop. This is one of the rare times I do recommend you give them the full story so they concentrate on the area that was damaged. Normally I suggest only sharing the symptoms and recent history, but not the previous repair estimates so as to not inadvertently limit or blind the second inspector into overlooking some areas.

I always made two printouts of the alignment, one to keep and one to put on the right front seat. I highlighted the angles that I adjusted. The computers allow for printing a number of different screens. Mine showed the "Before" readings on top that showed what the car came in with, and the "After" or "Current" readings on the bottom to show how it left when I was done. The "Before" numbers might provide a clue as to which part(s) might be bent.

Many shops don't provide those printouts because most people wouldn't understand them anyway, and some people get overly excited when they see a relatively insignificant number that isn't exactly perfect. If you didn't get a printout, don't fret, but if you think of it, ask if you can get one with the next alignment.

The straight steering wheel is just one observation. You also have to consider whether it pulls excessively to one side when you let go of the steering wheel, and that unsteady feeling. We call that, "predictability", meaning the sense you have that you know where to expect the vehicle is going to. Without good predictability, you have to constantly keep an eye on where you're going and be ready to make quick, unexpected steering corrections.

I'd still be more comfortable if the rear suspension was inspected closer.

Yes, it's possible, but it would take a significant hit. This is where I mentioned there could still be bent parts, but the rear alignment adjustments can have enough range to allow the wheels to be set back to their correct alignment values, as seen on the computer screen, but the suspension would travel in incorrect motions as the car goes up and down over bumps in the road.

If the people who did the alignment can't find anything bent or out of position, you may need to visit the dealer's body shop. They will be very familiar with this body style, and know exactly what to look for.