When I'm placing objects on tiles in my TileMap, they snap to positions that aren't on my tile's grid. I drag my object to the middle of the grid square, but it keeps snapping to the corners.
I'm talking about placing in the editor, not at runtime.
Godot snaps to the grid guidelines and not the cells between them. So you won't snap to the middle of the square that you're dragging to. That's because you're snapping the position of the object (that little symbol in the centre) to a grid, which is a specific position (the line).
For reference, these are the snap settings:

There are two aspects to solving this: your object's root and your grid/world settings.
When viewing a scene (like your player), if you click on the root node (at the top of Scene) you'll see a red cross indicating the root position. For side-view games, we want this on the bottom/feet of the object.

We need to align our grid with our world so it positions objects correctly.
