What does following animation represent for vacuum (quantum) fluctuation?

Question

On the page of quantum fluctuation, we have a gif representing some kind of fluctuation and according to AFT answer here $H$ which is $P^{0}$ and $P^{0}|vacrangle=0$ which would imply
$langle vac|H^2|vacrangle=0$
therefore $sigma_H=0$
So how come there is even any fluctuation? And why are arguments there heavily depends on virtual particle creation and annihilation when it's already told in the above mentioned answer that particles appearing and disappearing is wrong cause nothing happens for the state $|vacrangle$ as we translate it in time and space.
And if someone wants to point running my argument for Casimir effect the key difference there is: we change the system from one configuration to another and the net difference between the system leads to Casimir effect.

Cosmas Zachos · Answer

What is being depicted on that page is Leinweber's QCD lava lamp fluctuations of the action density (and also note his topological charge density fluctuations!), a functional of quantum fields,

cf his paper, in the  QCD "vacuum", really a ferociously non-perturbative condensate of gluon  fields & quark-antiquark pairs (operator fields), already having broken chiral symmetry (so, then, degenerate!).
The "vacuum" of this peculiar QFT is a ground-state medium state. This "lava lamp" graphic was used by Wilczek in his 2004 Nobel lecture to illustrate the surprising properties of the QCD ground state. It is simply not true that all QFT operators acting on it vanish identically!  People compute their v.e.v.s in lattice gauge theory simulations of the functional integral of this QFT.
The zero point energy of the QFT itself, a repackaging of umptillions of coupled oscillators, is a fraught subject; and grown men have  wept over its cosmological constant implications. In any case, these are not quite energy fluctuations. They are quantum field functional fluctuations in vacuum.

What does following animation represent for vacuum (quantum) fluctuation?

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