My very inexpert suggestion is to clean out the sides of the separation, then stain them, oil them, then brace the two sides to avoid further separation. You have more than enough wood for screws and a bracket. I wouldn't try to repair (fill, etc.) the current separation -- you're very skilled but I suspect it would wind up looking like a modern repair. However, I would definitely repair the sewing machine base's separation as this might increase due to the machine's vibration, among other causes.
My $0.02 based upon what I see in the pictures and my level of woodworking skill (which is nil).