Could a baby born with an extra thumb and third nipple be a surviving twin of the vanishing twin?

Could be but not because of the extra appendages. IE, my wife has told me that she was the surviving twin, the other vanished. The defects are probably just that, defects. Some got screwed up in the gestation and the child has an extra thumb and nipple.

Polydactyly (extra digits) and supernumerary nipple (extra nipple) are quite common and would not be the result of a vanishing twin.

Yes there is a possibilities

No.

Mammals as a whole are bilaterally symmetrical. So what is on the left is mirrored by what is on the right, there is PRECIOUS few places on the body where this isn't true. The number of mammary glands is roughly equivalent to the number of young that's expected during a pregnancy. Since we only have one child per gestation, then we have one set of nipples. Cats and dogs have litters so they have more. When you have a third nipple, chances are something went a little wrong during gestation.

Hands and feet are strangely similar in mammals. Five digits per appendage. When something goes sideways during gestation then you get more, as in this case, or less, as in one of my friends with two fingers and a thumb on one hand.

If a split embryo rejoins, it will follow a more logical defect, i.e. conjoined twins. You won't see it express as a little bit on the chest and a little on the hand.