Stoneskin turns flesh as hard as stone, not into stone. Technically it doesn't need any kind of visual effect. It needs a CLANGG sound effect as weapons bounce off the hardened skin, and a *resisted* indicator.
I can only hope Larian can resist the urge of applying a literal stone texture all over the character model just because they can and the spell has the word "stone" in it.
The way Stoneskin is explained is much more elegant and sensible than actually turning a character's skin into stone.
Barkskin on the other hand does make the skin have a "rough bark-like appearance". But only skin. Not armor, weapons, shields, cloak...
