If you sous vide for a long time, the entirety of the steak will be at the same temperature, while pan searing cooks the outside to a higher temperature than the inside, which results in the core temperature going up a few degrees during resting.

Yes exactly. It all has to do with the thermal conductivity of the meat. Meat tends to be a fairly good insulator which means it takes a long time for heat to conduct through a thick piece of meat (such as a large roast or a pork shoulder). This means that cooking at a temperature above your target internal temp (most conventional cooking methods, not sous vide) will produce a fairly steep thermal gradient between the outside of the meat and the core. Resting the meat allows heat to flow down the gradient to bring the overall temperature closer towards equilibrium.

Another important effect during cooking is the breakdown of collagen fibres (present in tough connective tissues which make some cuts of meat very tough to chew). This occurs in the presence of moisture at temperatures above 170F. When collagen breaks down the meat tenderizes and the collagen itself turns into gelatine which absorbs moisture and retains it within the meat. A gelatine-rich cut of slow-cooked meat (such as oxtail) can be very sticky and packed with flavour. This is one case where food can taste juicier with longer cooking times.

This is not a very quick test because you can hold sous vide food up to 4 hours at the target temp. So you will need to account for that 4 hour gap in all the testing before it starts to break down.