BoxCutter not cutting thru model. Only goes slightly into it

I think it is because you have snap turned on. It is trying to snapping to the face/vertex you are trying to bool in to.
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I turned off snap, selected your Cutter.002 object in object mode, and slid it down on the Z axis. Then to fix the edge, in Edit mode select all, hit ALT+N and “Recalculate Normals Outside” and it will fix those weird edges.

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also the thing you are booling with is huge:

consider this:
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