Sure, just get the slider constraint and mutate it:
https://esotericsoftware.com/spine-api-reference#Skeleton-findConstraint
https://esotericsoftware.com/spine-api-reference#SliderPose-time
Roughly:
Slider slider = skeleton.FindConstraint("sliderName");
slider.Pose.Time = 0.5; // Animation time in seconds.
It's easy to get confused when applying many animations, so remember that the skeleton is posed (by animations usually, but also app code) then during Skeleton updateWorldTransform constraints are applied in constraint order. A slider is a constraint, so that is when its animation will be applied. That means a slider can stomp changes made by animations or app code, which is usually the confusing part. Using Additive can help. If you fail to be confused enough, you can have slider animations key other sliders. 😉
Also the 4.3 pose system is new. The slider has a "pose", which is the unconstrained pose and is what normal animations modify. Skeleton updateWorldTransform determines the "applied pose" which is the pose after constraints have been applied and is used for rendering. App code can access either the pose or applied pose, depending on what you want to do.
The reason we need 2 poses is that we don't want Skeleton updateWorldTransform to mutate the unconstrained pose. It is valid to updateWorldTransform any number of times and the unconstrained pose doesn't change.
