It is the other way around. The sweet potato is natively from America, but it made it to Polynesia, unclear how.

Is it the same "Tombez Potato" writers of the 19th century report as being commonly grown and consumed in the Pacific Islands like Marquesas?

The fact that the leading theory of anthropologists for a long time was vegetation rafts is laughable in the face of the distances Polynesian people regularly traveled, it speaks to the parochial nature of much of the field.

Sweet potatoes found in Polynesia diverged from their ancestors in the Americas 100,000 years ago, long before the islands were colonized by humans.

https://www.nature.com/articles/d41586-018-04488-4

Also, the fact that many Polynesian languages used nearly the same word for "sweet potato" as some South American languages (kuumala -- Polynesian vs. kumara/cumal -- Quechua) is kind of a clue, yes?

The fact that the "vegetation raft" theory persisted for more than a few seconds in the face of this knowledge always astonished me.

Not just nearly the same. It's literally kūmara in Māori.