How to repair rust damage on my kitchen sink (pictures included)
It's an enamel coated steel (verify with a strong magnet).  There are DIY repair kits, but your rust looks pretty serious.  You'd need to start by taking the sink out, using a grinding wheel to get down to bare steel, then building up epoxy/enamel repair.

Yours may be a builder special of low quality: and the rust looks pretty bad.
I'd recommend a new sink.  Recycle the old one as steel scrap.  And caulk the new one well to avoid water pooling under the edges.