God's Compensation/Lore/Phasing and invisibility

As a 4D being begins to change their 4D location and distance themselves from the 3D plane they are currently interacting with, people and objects within that 3D plane will begin to interact with them differently. By just changing their 4D location by a small margine, they could still interact with the 3D plane while having some of the laws of physics changed in regards to them. Specifically, they can become invisible or "pass through" certain objects.

In default, these two things would actually happen together every time they step off from the 3D plane. It is something of a parlor trick that is a testament of the 4D being's skill to isolate one or the other.

Invisibility

In reality, becoming invisible is like stepping around a 4D equivalent of a corner so that people can no longer see them. A 4D being who is invisible in this way may or may not be able to still interact with 3D objects, but in some cases their limb might become visible again at the moment they touch a 3D object depending on their level of skill at positioning themselves relative to the 3D plane. Objects they pick up may also be dragged out of the 3D plane and become invisible as well. In all cases, while one is at this exact distance outside of the 3D plane the 3D beings on that plane can still hear them.

3 dimensional people or objects that are dragged just off from the plane by a 4D being in this way do not have the ability to get back on their own. They will be stuck in whatever state they are left in until a 4D being comes along to fix their 4th dimension location.

Walking Around

To a 4D being, a 3 dimensional wall is about as much of an obstruction as a flag-pole. If they chose to step off on an angle to the 4D plane, they will be able to "step around" a solid 3D wall in about 95% of all cases. Occasionally there might be some form of obstruction at other 4D locations that block this, but it does not occur naturally very often. Normally for a wall to be impenetrable to a 4D being, the wall has to have actually been built in 4 dimensions witch is something that can only be accomplished by another 4D being.

Phasing

Phasing is a trick where a 4D being will "walk around" an object on the 4th dimension, but do it in such a way that they remain visible to the natives of the 3D plane. Like this, a 4D being can appear to pass through a physical object from the perspective of a 3D being. In reality, what is actually going on is they are doing the equivalent of holding a prop-sword under their arm-pit to make it look like they were stabbed. They are doing this by moving around the object on the 4th dimension while being careful to make sure they are still visible to the native 3D beings.

It takes some skill to remain visible to the 3D beings while doing this. In the case of less skilled individuals attempting to "walk through a wall," the 3D beings in one room will see them as having become invisible and vanished from sight, and then they will seem to suddenly appear in the middle of the other room.