based on the lugs on your key switch I would say its probably 30A.
the wires you are showing look like 12ga, which can handle ~20a in short runs, maybe a little more. modern ignition wiring is almost 10ga, so probably 11?
wire gauge is like steel gauge, the lower the number the higher the capacity, so 12ga is the same as having 6 20ga.
its worth stating that fuses are there to protect the wire, not the equipment, so the max current of a wire is reflected in the fuse size.
you can rebuild that socket, a lot of companies make a bulb base repair kit, or you can use a replacement. search for 1156 which is the single filament bayonet mounting bulb type. here is one I found quickly
https://www.amazon.com/iJDMTOY-Wirin.../dp/B008DXRJN2
remember that your current socket grounds through the base in contact with the sheetmetal. newer sockets may have a separate ground.