Scratch it a bit with a knife edge or file if you want to know what kind of metal it is. I think below that silver coating, it’s probably copper or brass. Not sure brazing or soldering is going to hold… Going to be hard to solder or braze that crack back together stronger than it originally was when intact.
I may be crazy, but I think I’d drill a hole through the crack near the top. Push the pieces back together before drilling to make the crack as narrow as possible. Then put a short bolt in, a flat washer on each side, and a nut on the back and tighten it down as a clamp to hold the pieces together. Then you can do your soldering or brazing.
My first choice would be to find that part either new or at a salvage yard and just replace it, though.