Probably stamped sheet steel coated in porcelain like the old bathtubs.

The problem spots in those porcelain over stamped steel sinks are around the faucet holes and the drains ... I see rusting out at the faucet holes, which may make it impossible to install a faucet.

Check under the drain - remove the fitting - and make sure it's not too rusted out to hold the fitting.

If it's rusted out, I doubt they can be repaired, although there are some great epoxies for mending metals.

Porcelain usually refers to a glazed vitreous finish applied to ceramics. When a similar vitreous finish is applied to steel it is commonly referred to as being "enameled" so this is usually called an enameled steel sink top.

Google enamel or enameled steel restore repair. There are kits available and companies that refinish enameled steel sinks and tubs.

You can have a company re-enamel the sink in any color you like, and it will look beautiful. IF the sink hole is rusted out, it is easy enough for any metal guy to reinforce it and make it good as new.