Recently I was watching the famous "Powers of Ten" video which starts with a
I love that video! Thank you for your excellent question.
Of course, you are correct in saying that there is no sharp demarcation between the hand and its air around it. A water molecule that is part of the hand may at some point evaporate into the surrounding air. There is no particular moment at which the molecule leaves the hand and becomes part of the atmosphere. Its chemical bonds to other "hand" molecules weaken gradually, its distances from those molecules increase gradually, and even if these quantities do not change continuously (in the mathematical sense), there is no magic bond strength or distance at which the molecule officially leaves the hand and joins the air.
That being said, the fact that there is no sharp distinction does not guarantee that there is no distinction at all -- that "separateness is an illusion inherent to the experience of beings at a macroscopic scale". After all, there is no sharp distinction between night and day -- yet night is not the same as day. It may not be illusory to think that some molecules do not belong to the hand, some do belong to the hand, and some occupy an intermediate zone (a "gray" area). Separate entities can exist even if there is such an intermediate zone.
Moreover, in the course of solving a given physical problem, we might have to make more explicit what the difference is between the hand and its surrounding air. We might have to stipulate that a molecule belongs to the hand if and only if it feels a force greater than x towards the interior of the hand. Such a sharpened-up distinction may be somewhat arbitrary in the specific x chosen. But it might be serviceable for the purposes of a given physical problem. There might be a range of equally good ways of demarcating the hand from the air for the purposes of that problem. I'm not sure that such a case is best characterized in terms of separateness being "an illusion".