Drywall vs hardiebacker
HardieBacker on the studs, no drywall. In this zone the tile will hold better and last longer. Outside the damp or wet area, I change to green or blue board - a water-resistant type of sheetrock that I use in bathrooms. I will use HardieBacker for the width of the sink to the next stud, or in a tub / shower area, then green or blue water resistant sheetrock.

I have seen water-resistant sheetrock hold up for 30 years and even regular sheetrock for 20 or close with well-sealed tile. I have never had a quality cement board fail or need repair so this is the best in my opinion.