As of Scarlet and Violet, there aren't any. Some Abilities, such as Lightning Rod, raise stats after being hit by a certain type of move. Others raise stats after another Pokemon faints, such as Soul-Heart. However, there are none currently that raise a stat when using a certain move or type of move.
There are some Abilities that stretch this definition -- they boost stats or moves through other means. For example: Overgrow, Blaze, Torrent, and Swarm increase the power of moves of their respective types (Grass, Fire, Water, Bug) by 50% at a given HP percentage, but this isn't technically raising a stat. Guts increases the power of physical moves by 50%, so using physical moves could be construed as increasing your damage output.
Sources
Stat-raising Abilities (Bulbapedia)
Stat-increasing Abilities (Bulbapedia)