How do you deal with a gap between vanity and wall?
A semi-flexible trim such as a real wood or PVC quarter-round could be nailed to the wall, following its contour and concealing the gap. Because this is a wet area, definitely don't use an MDF type trim.
If not trim, then caulk. Silicone caulks usually aren't paintable but latex caulks are. A bead of latex caulk painted with leftovers of the wall paint might be less noticeable than the dark gap with dust and crumbs collecting in it.