The hunger bar will not update the current displayed hunger level based on the hunger reduction (or increase) from regenerating health. This is most noticible in a situation where you eat to overstuffed and do not perform any stamina draining actions. Your hunger goes down as it regenerates your SHP, but since none of it was used to regenerate stamina there is no change in the visible hunger bar.
The game does still track the change and will allow you to switch back to normal walk speed once you are no longer overstuffed, at which point your first step triggers the update since it drained some stamina. (crafting, building, and carrying things also triggers the update for the same reason)