Though, as for American Godzilla productions, there also were the comics and animated shows, as well as a couple of novels. It wasn't limited to the movies.
Yes, but American depictions of Japan (and Japanese depictions of America) tend to be inaccurate, caricatured, exoticized, and inauthentic. So I'm reluctant to count American cartoons or prose works set in Japan as actually "including Japan." To me, inclusion means involving actual people from the culture in the creative process. It always disappointed me that the 2014 film didn't actually film in Japan or cast native Japanese actors to make its Japan scenes authentic. I hope the new series will do that.
I think the first MonsterVerse comic,
Godzilla: Awakening, did a decent job with its depiction of Japan, but not a flawless one. The lead character, a survivor of the Hiroshima bombing, was a bit too quick to forgive Americans for it and join Monarch. And there's a page showing Mt. Fuji remaining essentially unaltered over 250 million years of geological and evolutionary change, even though Fuji-san is an active volcano only
a few hundred thousand years old. It also shows the Hiroshima atomic blast being visible from Mt. Fuji, when they’re actually about 700 km apart. As for
Godzilla: Aftershock, a G:KotM prequel, it also makes a decent attempt at depicting Japan, and like its predecessor, it gives its main monster a Japanese name, but it consistently misspells
Jishin-Mushi (Earthquake Beetle) as
Jinshin-Mushi, which is irritating.