Why is Nami considered a Vastaya?

This fellow, they get it.

Bloody hell you should see some of the vastaya tribes. Weird as shit.

Well, current paleontological evidence point to whales and dolphins having originated on land, then moving back into the sea. If whales and dolphins, then why not some branch of humans?

There are islander cultures that are very at home on and in the sea, some having divers that can hold their breath for prolonged periods of time. It's not entirely unbelievable to think that some island people would grow accustom to eating food harvested or grown from deeper in the sea, slowly becoming more adapted at living there. If food on their island slowly became harder to cultivate, but they could still get by living off the sea, it might push them back into the sea.

Yes, they probably wouldn't look quite so humanoid as Nami, but the general body shape and hands would probably be similar to ours. Of course, if you're willing to accept Magic into the process (which you'd have to in order to accept the "shapeshifting creatures who were greatly in tune with Ionia’s natural magicks" which helped create the Vastaya) then you could probably get something decently human like without deity interference or fish mating in exchange for a much longer evolutionary history than that of the Vastaya.

TL;DR: If you want Nami's species and culture to be relatively young, the Vastaya explanation is fine. If you want Nami's species and culture to be older and more mature, then you can get there via evolution plus a little magic for cosmetic effect.

She is.

However, Runeterra has no words for "mermaid" but they do have a word for "half human, half animal" with that being Vastaya.

Vastaya = animal ppl

*Chimeric ppl.