Very loose rear end (Handling)
 

So the short of it is my last set of tires I wore down till they were nearly bald and then I ran over a nail so I had to write on a donut for about a week. I just got new tires installed Kumho ecsta31 and now my car sways like a boat on the highway. Anything above 45. Any thoughts?

What size are the new tires? did you do all 4?

This ^


And if you did are they on facing the right/same direction. They are a unidirectional tire so if not all on properly you will get exactly the results you described.

I always thought new tires were always more "floaty" since there's a thicker layer of tread than the outgoing bald ones to move around on.
New tires do need to be worn in too to wear off the mold release on them. It could also be the new tires sidewall is softer. Tire pressure too
low after they installed them also could be a culprit. I just had mine installed and the put 3 at I think 35 psi and the 4th one at 55 psi.

when i put on a new set 6 months ago, i had that floaty feeling for a few dozen miles, mostly on the highway when changing lanes. overtime either my senses were recalibrated or the tires broke in to some extent, it is no longer noticeable.

Wouldn't riding with a donut on the rear for an extended amount of time cause some harm to the LSD?

Since they are new tires, maybe the mold relase.
https://tires.tirerack.com/tires/Mold%20Release

Otherwise check tire pressures.

The tread should make a difference since although there is more of it should also be sticker so not moving around. The release fluid may make it a bit squirmy for a few miles but doesn't last long and should not be extreme. The softer sidewalls could have some initial impact to feel but should noy ake the car "sway like a boat". The pressure could very well come into play though if not set properly.

Yes. The manual states that if you have to use one you must use it on the front and move the full size to the rear.

Had the same issue this past winter when I dropped off my stock wheels to my mechanic to have him mount my snows for me. Now obviously snow tires are going to feel squirmy compared to my summer tires, but the car was floating all over the place at highway speeds.

Turns out that I shouldn't have assumed that he would set the tire pressures properly. All 4 were different pressures. One being almost 50 psi!

I am starting to wonder if I have the only fully competent tire guys around! I think I will go give them a hug.

You replaced $180 high performance summer tires with $80 all season tires, it's not going to handle the same.
Edit: Oops missed the Ecsta part, so not a massive downgrade to all seasons, but I think a downgrade nonetheless.

Check the tire pressures, everything else people mentioned, etc. but at the end of the day you downgraded your traction.

The only thing not mentioned is alignment, maybe something slipped out of whack.

Don't hold your breath, just put 4 new tires on and they left the tires at 55psi. Always do your dudiligence.

I do and these guys have not failed me once in 9 years. Everything has always been spot on.