Waterproofing between wall and new sink vanity

Yep, PVC trim, Accent-strip Tile, Slices of a 12x12 (whatever size you desire) Tile or a sliver of Granite would probably be the best and not be problematic with future cleanings removing a finish or paint.

Or, you may want to reverse your thinking and frame around the entire mirror with a decorative PVC molding. This assumes the mirror is gapped all of the way around for the best look.

Although Iggy's advice would work, vanity tops often come with a matching backsplash (3-4" high). If this was a display model at the store, they might have left this in their back room or in the display vanity to prevent damage, and they just forgotten to give you it (or possibly the salesperson wasn't aware).

Otherwise, PVC trim is definitely the simplest option, but if you want something more decorative, you might ask around about discontinued tile samples, or consider using a marble threshold.