Kirk here. This article is fairly old now but I think the “stay tax” (宿泊税) is still in the works. The headline refers to the “negative effects of foreign tourism” but the article doesn’t explain those effects in detail. As far as I can tell from looking at a few Japanese articles, Kumamoto City needs to find funds to allow it to provide appropriate services for the growing numbers of visitors, but I’m not exactly sure what services are needed. At any rate, the tax would be a few hundred yen per hotel guest, regardless of citizenship.