The term that’s used sometimes to describe pitchers with this style is called, “ hookers”. Commonly, you’ll hear a coach say “ Joe’s a hooker” when alluding to a posture like yours. And as your picture shows, somewhat, is a style that resembles that.
Some pitchers perform in this way without any real problem. In fact a lot of these pitchers do it unconsciously without any deliberate reason other than … “ I just do it”.
With respect to performance problems, perhaps it does alter your performance, but without video of your complete form it’s hard to tell. I’ve had pitchers that do just that, but seem to perform without any issues – health, control, durability, etc.