Something that has come to my attention, is setting an entity's hand to AIR/NULL does not seem to apply, more specifically a Skeleton.
Spawning a new one, immediately setting their hand to null/air, their hand was still the bow.

After doing some testing, I came to realize, it is setting the hand to null, it is just not syncing with the client.
If I relog, the entity is updated correctly.

Test Code:
(I want to point out that I do understand one could use a consumer, this was just brought to my attention from a Skript user, regardless the slot should update)

Location location = player.getTargetBlockExact(30).getLocation();
World world = location.getWorld();
Skeleton spawn = world.spawn(location.add(0, 1, 0), Skeleton.class);

player.sendMessage("Before: " + spawn.getEquipment().getItemInMainHand());
spawn.getEquipment().setItemInMainHand(null);
player.sendMessage("After: " + spawn.getEquipment().getItemInMainHand());

This code is included in the provided plugin. Simply load this on a server, point to where you would like to spawn a skeleton, and run command "/test" in game.

As you can see in the picture, it tells me the hand is AIR, but you can still see his bow.
When I relog (see second pic), you can see it is updated correctly.

This issue was just recently brought to my attention. I believe this worked completely fine in 1.16.4, but Im not sure when the issue came about.