Is it possible to tile over drywall to create a backsplash?
If your drywall is sound, then yes. My entire shower was green-board that had been tiled over with a mastic (not thin set) It rotted after some 40+ years, but you’ll have that. A typical back splash does not usually see the amount of moisture that a tub surround does. I would use a tile glue, not a thin set, on drywall (well That is how I installed my marble back splash). Silicone the joint between the counter and the back splash and seal your grout. If you want or need to use a thin set, I would agree with the assessment to apply a tile backer. You can get permabase and hardibacker (or is it dur-o-rock) in 1/4 inch thicknesses, screw it to the studs and proceed with the tiling as per recommended procedures.
