agreed this was to get the ball rolling:

perhaps:

struct Style : ChStyle<Style> {
    Value look[4];
    Color monocolor[4], textcolor[4];
    Point pressoffset;
    int   focusmargin;
    int   overpaint;
    Font  font;
    Image ok, cancel, exit;
    bool  transparent;
    bool  focus_use_ok;

    // Animation properties
  enum AnimationFinishBehavior {
        GOTO_FIRST,      // Go to the first frame when the animation is interrupted
        GOTO_LAST,       // Go to the last frame when the animation is interrupted
        COMPLETE,        // Complete the animation normally when interrupted
        COMPLETE_FAST,   // Complete the animation quickly when interrupted
        HOLD,            // Hold the current frame when the animation is interrupted
        REVERSE          // Reverse the animation when interrupted
    };

    AnimationFinishBehavior animationFinishBehavior;
    double animation_duration; // Duration of the animation in seconds
    double (*animation_easing_function)(double); // Easing function for the animation
};

and ChStyle perhaps:

template <class T>
struct ChStyle {
    // ...
    std::vector<T> animationStates;
    double animationDuration;
    EasingFunction easingFunction;
    // ...
};

obviously the drawing functions like ChPaint, ChPaintEdge, and ChPaintBody would need to incorporate the animation properties.
The BaseAnimation class could still handle animation logic and calculate the intermediate values

certainly the case of handling Mouse event (e.g., OnMouseEnter, OnMouseLeave)
would need to have some form of update to the animation system

void Button::OnMouseEnter() {
    // notify Update the animation state
    // ...

    // notify Start the animation
    // ...
}

void Button::OnMouseLeave() {
    // notify Update the animation state
    // ...

    // notify Start the animation
    // ...
}