As you can see, the handles of the square are snapped to the intersection of the grid lines. So it seems to be snapped properly.
But apparently the square has both a fill and a stroke. If you remove the stroke, there will be no overlap. Do you need instructions to remove the stroke?
I thought we had a recent new feature, which allows the stroke to be aligned differently relative to the path (along the centerline, the inside edge or outside edge). But I can't find it. Maybe it never has been created yet?
Edit
By the way, I meant to also mention that there are a lot more snap controls in the main window, in case you didn't know.