Years ago, when playing with active suspension (on a road vehicle), I discovered that the lateral stiffness of a tyre could affect the stability of a suspension. Basically, the vehicle could be made to "dutch roll"
. The issue was more pronounced with the vehicle stationary, and the "fix" was to halve the loop gains in this condition.
Later when rig testing real vehicles (road & race), a roll input at the contact patches generated two body modes, one with the roll centre below the ground plane (i.e. mostly translation), and the other with it above (i.e. mostly roll). Initially, I discounted the first (thinking it was caused static tyres). But later, when playing with options on a touring car I discovered that as bar/spring stiffness ratio was increased, and dampers followed the springs, the vehicle could (& did) go unstable in the middle of a corner. The cure was the go back a step, increasing springs & dampers and (I think) reducing bar stiffness. Lateral tyre stiffness was important in this case, and the damping ratio of the lower roll mode was a useful parameter during a rig test.
I suspect that the instability shown in the GIF was similar to that of the touring car (but at a different axle). It shows a mixture of lateral and roll tyre deflection (and probably a lot else). The motion couples with the sprung mass (at least aft of the engine bulkhead). The patterns seen on the loaded wheel, and the wake of the unloaded one suggests that the CPL changes were large. My guess would be that this was the stability that Raikkonen complained about (hence it affected more than one team).
My thoughts are that it is unlikely it would be predicted by a full vehicle simulation, that F1 engineers have generated designs that are difficult to work with (dampers are usually non-adjustable, and springs take forever to change), and who knows what has happened to the tyres. It probably explains comments like "we were quick & don't know why", or "we lost performance unexpectedly", etc.
I could comment on the "notorious Michelin standing waves", but not right now.