i did a google on "edwardian sewing machine parlor cabinets" and came up with several that were similar to yours. i did find a blog that is on old singer machines, and found a photo of the treadle mechanism, that cage-like part on the side. there might be something of value, photo-wise on the blog: it appears to be dedicated to restoring and preserving old singers.
https://oldsingersewingmachineblog.c...wing-machines/