> when entropy can increase no more, and there is no more possible change to occur

Even as the concordance model cosmos asymptotes to (vacuum) de Sitter, with fully evaporated black holes and less than one proton (assuming they're stable) per Hubble volume, there will be at least a sparse gas of cold photons from two sources: the relics (the cosmic microwave background) and the horizon radiation. A comoving observer, who has an isotropic view of these photons, would still in principle be able to detect the metric expansion in the spectrum of these extremely long wavelength photons. More vacuum being created means (Boltzmann) entropy is increasing: one can substitute microscopic sections of vacuum with each other and do so wholesale without getting anything but vacuum.

Importantly though, not all timelike observers in the ultra far future need to be comoving: they can be highly boosted with respect to the remaining sparse radiation, and can even be accelerated with respect to it. That means they'll see a dipole, bluer in one direction, more particles in the bluer direction. In turn that means have an easier time looking for the spectral signature of the adiabatically cooling relic photons and the horizon radiation, even if there is nothing else they can observe. (By Unruh and Hawking an ultra-accelerated observer could see and/or generate massive particles).

Therefore, "entropy can increase no more" depends choosing [a] a (large) subset of possible observers to the exclusion of others and [b] treating the cosmological frame as useful in picking out quantities like entropy when the sparse distribution of matter barely favours that frame's use. Neither is in the spirit of relativity. Switching to different set of coordinates can reveal an increasing volume of relatively empty space and a cooling of the remaining relic radiation and the relatively newer emission from the cosmological horizon (see Gibbons & Hawking (1977), Phys Rev D 15 or the sadly not very detailed <https://en.wikipedia.org/wiki/Gibbons%E2%80%93Hawking_effect>).

Therefore, in an FRW universe that asymptotes to de Sitter -- our standard cosmology -- there is no true vacuum state for a comoving observer, and there are many-particle states for various other observers. So at least Boltzmann entropy (S = k_B log W) can always increase and this increase is in principle measurable by whatever scientist is left in the almost void.

(Of course, our model cosmology gets updated from time to time with new discoveries, and it may turn out that we are not destined to asymptote to de Sitter, but at the moment as far as we know there is not much wiggle room without adding as-yet-unobserved features to our known universe.)

> video ... frame[s]

> no time was spent

The apparently paused frame (not much is going on in any direction) will grow from a very very dark grey (in the sense of "grey body radiation") to even darker grey while on "pause", as the (time-dependent) Hubble parameter decreases and as the CMB redshift (and the redshift of earlier-time cosmological horizon radiation) increases.

Ignored above: relic neutrinos, fluctuation theory and nonequlibrium statmech in general, observers with relativistic spin; these can all break the placidness of a far-future "tremendously low frequency" (sub-)radiotelescope's view. Also don't see much point in delving into speculative physics (like BTSM particle physics, quintessence and similar dark energy, or non-GR gravitation) looking for anything that undermines the above or which might support your analogy.