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If all of the suspension pieces check out okay then it could be a bad rack. Not an uncommon problem but you should have it diagnosed by a competent mechanic rather than just throw on a new rack.
It feels like there is slack in the steering wheel. It seems to take a while to engage the steering.
Try tightening the outer tie rod nuts first. My 11 GS with 12k miles
were barely snug from GM and caused issued. 18mm wrench and an allen (don't remember the size).
The first thing I would check is the feel of the steering when the car is turned off and sitting in the garage. Gently feel the steering as you move the wheel back and forth. If you feel play, then something is worn or (less likely) loose. If you don't feel play, then the issue is likely the alignment. Alignment can make a big difference in the way the steering feels on the road at speed.