Essentially what you are doing is using a Slot in Spine to act as a 'separation point' where the slots above it are rendered into one 'Parts Renderer', and the slots below it are rendered into another 'Parts Renderer'. Check out the SkeletonRenderSeparator: spine-unity Runtime Documentation: SkeletonRenderSeparator (there is an Example included in the unity runtime for this if you want to check that out).

You can separate a SkeletonAnimation into separately rendered sections, where each section can then have its own layering (Sorting Layer + Order In Layer). Or if you have other suggestions in order to solve this issue please let me know. If you know how to mask or change the order of specific Spine bones/slots after importing to unity I would love to know. I would also like to use these character in other objects where this type of layering might not be necessary, so exporting characters with premade clipping is also not the best option for me. Different types of tables are sometime half empty or full with different characters sitting in them randomly.

The reason that the table and parts are not inside the Spine rig itself is because the type of tables and characters change dynamically during runtime in our game. The character can only interact with masks as if it's one piece so the whole character is either in front or behind the tabletop and other parts. On the right is the same character imported with Spine. On the left you can see our old setup where characters are sorted and masked both among each other and with the table and chair parts.

Esoteric software spine masks