“Above” means at a higher level.
“Over” suggests directly above.
There is a noise coming from above.
The noise is coming from above my room. (Not over)
Put a blanket over her. (Not above)
In your example, “over” would make me think that the cabinets were directly above the sink, whereas “above” could mean that they are a higher level than the sink but perhaps on a wall slightly behind it. But it’s not precise and people could use either word for either case in that particular example.