The paper has nothing to do with polynesian or colonial era contacts. It's about the genetics of the people whose descendants would go on to populate the Americas and what they say about the routes they took to get there (pacific coastal route or inland).
I'm a bit surprised to see it here, this is a pretty niche subject.
three of those links are about the same study suggesting pre-colonial movement west from the south american coast towards polynesia, and one is about analysis of ancient remains.
this study involves a large genetic survey of modern indigenous populations not only along the coast but also in the interior of the continent, that suggests ancient movement from polynesia to the south american continent.
https://www.nature.com/news/dna-study-links-indigenous-brazi...
https://www.nature.com/articles/s41586-020-2487-2
https://www.sciencenews.org/article/south-americans-may-have...
https://www.smithsonianmag.com/science-nature/native-america...