Hi Anna.

I believe there is no backsplash. Just a tight fitting countertop with a narrow concave bead of silicone caulking. I would think the drywall around the vanity is water-resistant with a bathroom quality paint . Keeping the countertop clear of water would be important to avoid mold / mildew at that seam - not a detail for everyone.

Thank you, this helps. Aesthetically, I'd prefer clean look as you described and will proceed so. If it doesn't work, we decided to tile the whole wall afterwords. On the paint, I'll consult with our local Sherwin-Williams, unless you know what to look for? I have used their Duration line in Satin finish on my walls around the house and Semi-Gloss on Trim and Doors.

The issue would be in keeping a tight bead of silicone there in the intersection. Taping above and below would help. If the silicone get too thin at the edge it can start to peel after repeated cleanings and that could create the crannies for the mold/mildew to start.

Best of luck....