When you change an animation, GDevelop behaves in one of two ways. If the animation stays the same (so change to “walk” and it’s already “walk”), then GDevelop does nothing. But if the animation changes to a different one (like “walk” changes to “run”), then GDevelop will start the run animation from the first frame.
With this in mind, your problem arises because you are setting the animation to walking when the horizontal arrow keys are pressed, but to sprinting when the z key is pressed. Because the arrow key sets the animation to “walking”, when GDevelop get to the z key part, it resets the animation to “sprinting” and to the first animation frame. This happens every processing frame, or every single time GDevelop get to that event.
A quick fix is to add a subevent to each of the left/right key press events, move the “change to walking animation” actions into the subevents and add a condition to those subevents that checks the current player animation isn’t sprinting.