Wales, when independent, could reasonably be described as a nation state, being roughly associated with the Welsh people and their culture, language, history etc. But most countries are not nation states! The USA, Russia, and China for instance are explicitly plurinational.
If you think "nation" and "state" are synonyms (along with "country") then it's redundant to use both. If you think that "state" alone might lead someone to think of Alabama or Minas Gerais then say "nation". If you think "nation" will make people think of Cherokee, then say "country" or "sovereign state".
"Nation state" has a specific and well-established meaning, misusing it is like misusing any other jargon and just comes across as a failed attempt to seem part of the ingroup and hence authoritative.
(yes, apparently I will die on this hill)
A country that strictly limited residency by ethnic identity might be called an "ethnostate" and indeed it's hard to find a pure example of one of those.