The United States is not an ethno-state though. Maybe during its founding and in the past it was, but it has long stopped being so, despite the recent desires of some factions to want to turn it into one again.

Multiculturalism has long become one of the defining characteristics of the US.

Japan (and frankly, many other countries) are indeed ethno-states.

Comes down to the culture and ideology of the country.

Is the culture thinking being a X is race based or is it based on a way of life, or both?

At least back in the 80s and 90s, my US education and history books say that America is the melting pot of the world, and ideally not race based, but based on the idea of personal and religious freedom. USA as we know now began as a country of immigrants - so by definition, yes, USA still stands regardless of race and ethnicity.

Whereas, the older countries having a more homogeneous race, ethnicity, and culture, that question is a lot fuzzier.

America isn't a several millennia old, monoculture-ish country.

Edit: well, it was.

That’s essentially my own question. It’s not specific to Japan. Do you want to answer it?

USA with maybe Canada, is rather special case. In general other countries around the world are more or less ethnic, or at least have be big ethnic groups and somewhat shared cultures.