I doubt you really need every leaf to move on its own. If you do, you'd need a bone for each leaf. You can use a region attachment for each leaf, no need for meshes. That could make sense if the tree is the most important element on the screen, though many parts of a real tree move together naturally. Work from the movement you need and only make the skeleton as complex as necessary for that movement.
It's common that adding every possible detail doesn't fit within performance budgets. Look for ways to fake it! You can use bones to deform the whole tree, giving it movement without animating every leaf. Mix that with animating some of the leaves to get a convincing effect. A single image could have multiple leaves on it, possibly with blank space between them. Layer a number of those images to make a tree where many pieces can move, though not every individual leaf. You may be able to draw attention to one area of the tree, like a leaf falling off, which can allow the other parts of the tree to be simpler without looking bad.
Ever see the "trees" in Super Mario? They are highly stylized and simplified, but they work well.
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Also instead of attempting to be realistic, the trees dance. If you look closely, they don't just dance randomly, they are synchronized to the music!
While Spine does a lot with skeletal animation, don't be afraid to mix in frame-by-frame animation. A tree can be a large element, so you may not have a lot of frames to work with or you may want to restrict frame-by-frame to an area smaller than the whole tree.
If your scene has multiple trees, at runtime you can pose a single tree and then draw it multiple times. This way you can have say 10 trees with unique poses, but draw 100 trees and user are unlikely to notice they are not all unique.
