Wheels are stiff, tires are not. A larger wheel - and smaller tire sidewall - will have less side-to-side flex and vertical deformation in corners and bends in the road. The handling improvement is mostly apparent when the driver is in "sport mode" - not a typical behavior for a standard-issue ID4 owner. It makes a big difference in evasive-maneuver situations, but during those split-second events there are many other factors that are usually more prominent.
None of us is likely to make the effort, but I'm sure a pair of drivers with the 2 wheel sizes could do an A/B comparison at a Car Control Clinic, and would quickly learn to spot the differences every time. The most important variable is the driver, but in successive runs with each car, you (and the observing instructors) would the difference in measurable ways.
I find it odd when wheel-size packages do not also include some mention of suspension upgrades: a stiffer wheel/tire combo should imo be accompanied by a stiffer suspension, or a significant part of the upgrade is lost to body roll and steering geometry. Makes me think that the suspension is tuned to one wheel size or the other and we just don't know which.