Hello FoG!
From time to time, this topics pops out, so let me gather the resources we have about it here.
Let's talk about adding poses that are different from the ones you have in setup mode, such as in the gif above.
Some people decide to create a different set of bones for alternate or rotating poses, this is the first approach, but as easy as it may be to set up, because you activate a pose different from the setup pose, add a bunch of bones and turn the correct set of images during the animation, this also quickly becomes hard to use the more special poses you decide to add to your rig.
To avoid this problem some people thought they could add these new sets of bones to different skins as skin bones. And yes, skin bones will only be present when a skin is active, but skins are not something that can be animated inside the editor, so this is not a viable option, nor the intended way for skins and skin bones to be used.
A more ideal approach is to attempt to reuse the same set of bones for different angles. This is more practical when animating, as Spine will come in help with bones interpolation, impossible if you replace skin or set of bones like the attempts above, but a little less intuitive if it's the first time you try to do this.
I've covered some different approaches to turnarounds in Spine during several streams on Twitch. I recommend downloading the projects first, then finding a topic you'd like to know how it was done and using the chapters at the side of the video to jump straight to the part where this is being done.
Spine: Twitch
For example, here's a gif that shows the final result of creating a turnaround animation for a cat rig first, then reusing the parts to create new attack animations:

Here's a character walking in 8 directions while changing assets at every direction change:

Both examples can be downloaded from the page I link above and overall, the technique relies on these key aspects:
- Only one pose is present in the setup pose, usually the more frontal one
- The other directions are collected in Animate mode inside a turnaround animation
- The Preview view is used to help to realign the pieces of the alternative poses
- Update bindings is used to rig the meshes in the poses stored in the animations
You can either decide to draw all the possible rotations of the body and create turnarounds for every single piece to rotate around the axis of their bone, or you can sketch the poses first, then realign the bones as shown in the videos of the second gif:
Spine: Twitch: video fw vY6pHjJE
I'll close this post with a couple of nice examples from other people who did this as well:
Misho and Robin - TV animation series
DISTURBING THE VERSE - zero-gravity fighter!