I would guess you must have the suspension heavily tuned (to defy the laws of physics - "regardless of which drive mode I’m in" - DSC fails to help?
).
Don't contemplate whether the tyres are runflat - just check it (it's weird if you don't know what tyres you have
). I use runflats but I don't experience anything like you describe. Also check the tyre pressure (I've run on two overinflated tyres on one side from a tyre shop
but that failed to affect handling noticeably).