With nonessential checked, the mesh edges are in the data. These are the connections around the hull and the connections made manually between vertices inside the mesh. Internal edges are normally created to control triangulation. Runtimes use the triangulation from the skeleton data, so edges are not needed at all, which is the definition of nonessential data. Internal edges may also be created because the animator likes how it looks, or wants to manipulate parts of the mesh and edges make it easier (especially when you select an edge while holding shift, for edge loop selection), eg the orange lines here:

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If importing data with nonessential unchecked, Spine recreates the edges around the hull but it doesn't know about internal edges, so they are lost.

Nonessential data shouldn't cause a difference in the hull or UVs. Maybe its changing the image sizes that is causing it? The mesh image width and height is nonessential. Loading the data without knowing the mesh image width and height might change what Spine does when you change the images. Eg, if you let Spine load the larger images, it then knows the mesh images to be the large size, then when you replace them Spine will apply its resizing logic (which we know we need to improve). If you give it the resized images without it ever seeing the large images AND it doesn't know the expected image sizes since your imported data didn't have the nonessential mesh image width and height, then likely it won't apply the resizing logic.