I'm not really sure. I'm kinda new to Unity so I don't know how other plugins handle it. 🙁
If it helps at all, I don't think the ability to change the animation clip in the Inspector UI dropdown while the game is running is either super useful or standard. Unity's own native animation component UI doesn't behave like that either, as far as I know. It just allows you to set the initial animation.
In which case, the AnimationState could just be the authority and the string-sync could stay if you wanted the Inspector UI to at least show what animation is currently playing in the inspector while the game is running.
Alternatively, you could also just change the field in the UI to say something like "Initial Animation" and use the string only once to set the animation in on initialization— ie, SkeletonComponent's Start() method.
A third option might be to have an extra boolean that's accessible through the UI which switches authority between the string and the AnimationState, but give priority to the AnimationState by default. This way, we could keep the animation changing-on-the-fly-through-UI feature.
I guess your worry was still standardization and a clean interface, but I'm getting the impression that you'd be the first, or one of the few, to actually implement an animation changing through UI feature.
Again, that's just me. I definitely think other, more experienced people need to weigh in on this.