Got lemons? Make lemonade!
Maybe this is a crazy idea but here goes.
Your cleaner is basically lye. By the original color of your sink and the color it turned I would guess it is either bronze or patinated copper. The copper color it changed to is not terrible; the only problem is that it does not match and it is irregular looking.
Roll with it. Get another bottle of the same stuff and treat the entire sink with a smooth coat. Spread it around with a sponge brush. Wear gloves and goggles. Let the drain cleaner sit on the dark areas and do them like it did the spot near the drain. Then rinse and buff it out.
You will have a copper colored sink. It is not going to look worse than it does now. It will cost a bottle of drain cleaner and a sponge brush to try. If you get away with it and the sink looks good, you are set.
If it looks terrible, it does not close the door to trying something else with the sink. On the theory that alkaline turned it bright, you could try acid to turn it dark (lemon juice?).
If you do try this please post image.