Yes, AFC Single is a much better focus choice for small birds that aren't filling the frame and that are not moving. I did some experiments and my pictures got much better.
Also the camera clearly focused on the branches at the bottom. Focus systems have a hard time with meshes and patterns. And it will usually focus on the closest thing with highest contrast. So the branches fit that bill. You have to be a bit more careful in AF on a bird in a tree. And doing a focus override will really help. That and a good stable platform. If you're handholding and swaying even a little that can throw off good focus.