The other thing that can make that floating feeling in speed is wheel hub bearings but I doubt it. Worth checking though.Welcome and sorry to hear the car is unstable at speed. That’s def not normal.
I would also be surprised if it were from the aero as what you have is not capable of that much DF. You can test that though. Pull the wing and splitter off and try it out. If the problem persists my money is on alignment.
also go through all the suspension bolts and make sure torque is good.
BC coils are not great but unless they’re completely blown they would not create a floaty feeling at speed in a steady state (damping wise).
Also it getting worse with the new tires makes me think alignment. These cars can “tram line” badly with certain tires and alignment settings.