That's it after wire wheeling. I can't see any maker's marks nor a size. I think it might be imperial, I've not got my good calipers to hand. The recess is about15mm deep.
Yes, IIRC as a tool kit to change out a vehicle tire, there would be a round bar to fit thru
the cross hole, might even have a chisel shaped end to double as a tire iron.
I've checked for markings squinting through a loupe. None to be seen. The larger hex is 25.8mm, the smaller is 23.4mm, that suggests BSW to me. The tommy bar hole is 14mm, too small for a jack handle I'd say.
I've more of them in the rusty tools boxen. I'll clean them and check the sizes.
What diameter is the blind hole in the picture? If it is to accommodate a projecting thread, it is quite small compared to the nut A/F. If it is too small for a thread to pass, then that limits the application of the tool to something that does not have a projecting thread.
The A/F sizes do correspond with 1/2" and 9/16" BSW.
The blind hole is about 10mm and reaches the tommy bar hole. The roughness of the hole suggests it's part of the casting or forging stage, it's not machined by the look of it.