Mine is the same way. Bought it this year with 154K mi. and was stock height. Put basically a 3”/2” on mine with 5100’s front and back and Eibach front springs and super flex rears. Right after I lifted it, it felt very floaty as well and that was with the exact same tires and wheels so I compared apples to apples. With new tires (bigger) and wheels it still felt exactly the same so it’s not my tires like some say. It felt pretty sketchy on the hwy or fwy and still kinds does.

I did replace the rear sway bar end links with Moog 2nd generation (1”longer than our 4th gen) More Information for MOOG K80380 and energy poly bushings. This definitely helped some as it stiffened it up a bit and helped bring the rear geometry back a bit. After that, I did a sway bar relocate kit and drop as well as energy poly end link bushings and sway bar bushings. Didn’t notice much improvement in squirellyness there but feel the bumps more so may have helped a bit. It still floats and I know exactly what you mean. Not sure if somethings wrong with mine either. I just deal with it now and try to pay very close attention to the road, if not I have a tendency to end up on the other side pretty quick (happened just a few hours ago lol!