I am also facing this issue right now. I have scenes that share some common animated objects. e.g. grass, trees, birds, etc. I try to drag the bone to another skeleton from another scene but only the bones and images are copied. The animation is missing. Is it still not possible to copy single animation of a bone or mesh across skeletons in a project?
By the way, I have another more powerful idea for the situation. It would be awesome if Spine has something like asset library. I could select a bone of the project, give it a name and save it as an asset. All the stuff including animations and images under that bone would then be saved as a package. On another project, I could search the library, choose the asset I want and import. It restore the package under a selected bone or replace a dummy bone. That would make copying items between projects (or even multiple spine applications running simultaneously) super easy.