This is a very interesting plane! I don't think this is a woodworking plane. Although it would be nice to see a picture of the sole and blade, it does not appear similar to any scraping or toothing plane I've ever seen. It would also be nice to know the weight of the plane, and the width and configuration of the iron.
Peter McBride is tremendously knowledgeable and clearly he has done significant research on his plane that is quite similar to yours. The section in Holtzapffel's book that McBride links to shows a picture of a plane that appears identical to yours, along with the following text:
The smith's-plane for brass, iron, and steel, fig. 330, has likewise a perpendicular cutter, ground to 70 or 80 degrees; it is adjusted by a vertical screw, and the wedge is replaced by an end screw and block, as shown in the figure, which is one-eighth size. In the planes with vertical irons, the necessity for the narrow mouth ceases; and in the smith's plane some of the irons, or more properly cutters are also grooved on the faces, by which their edges are virtually divided into several narrow pieces; this enables the instrument to be more easily employed in roughing-out works, by abstracting so much of the width of the iron, and by giving it a greater degree of penetration, but the finishing is done with smooth-edged cutters, and those not exceeding from five-eighths of an inch to one inch wide.
Note the use: for "brass, iron, and steel". McBride notes that his plane weighs over 6 pounds. This makes sense for a plane used to cut metal, and is far more than the weight of typical woodworking planes for scraping and toothing. Note also the angle of the cutting edge; 70 or 80 degrees for a 90-degree bedding angle makes sense for metal, but would probably not provide enogh clearance angle for wood. Note also that the use of a grooved iron for "roughing out" is mentioned: this makes sense for metal, but not for wood.
Jim Bode has a similar plane listed on his website (
https://www.jimbodetools.com/products/rare-holtzapffel-toothing-plane-92469u) which he describes as a toothing plane. He lists "Russell, ANTIQUE WOODWORKING TOOLS, page 371" as a reference. Unfortunately I don't have this book and it is not easily available.
Although Bode describes this as a toothing plane, I am skeptical. I am not aware of any toothing planes with an iron this narrow (7/8"). if you have ever used a toothing plane it is hard to imagine why someone would build one that narrow; they more typically have 2" irons. Additionally, if narrow toothing planes were useful then I'd argue that someone would have produced them in the form of a standard wooden molding plane.
I believe what you have there is a very rare and unusual plane, and an important historical piece. As such I would recommend no restoration whatsoever, at least for the moment.