In general, identity nouns seem to be trending out of use in favor of adjectives (modifying “person” in the most generic, simple case), so the cases where existing ones fell out of favor more completely because of other problems are probably not likely to see general replacement, and even the ones that persist see less use over time with adjectives modifying some other noun being more frequent.

When referring to someone other than the writer/speaker, some see them as problematic because they can be othering/dehumanizing, or they can suggest a (potentially incorrect and offensive to the subject) priority of the particular axis of identity.

Does that mean that I need to introduce myself by saying "I am a Japanese person"? Should I request my colleagues to say "I am an American person" when introducing themselves?

Usually native speakers would prefer the adjective rather the noun in these cases ("I am Japanese", "I am American"), or the prepositional phrases ("I am from Japan", "I am from the U.S.").

Where we don't have a subject pronoun to which the adjective can be attributed, we would usually supply "person" or another noun referring to a kind of person ("A Japanese person told me...", "Any Chinese person would readily recognize the meaning of hundreds of kanji based on the influence of hanzi", "My friend married a Japanese woman", "My mother goes to a Chinese acupuncturist").

I think it's because Japanese and Chinese are nationalities that have been long known by the wider, more xenophbic populace. And they are also used as catchall terms for Asians. For example, the first episode of King of the Hill where the Texans meet Kahn, a Laotian, and Dale repeatedly asks if that is Chinese or Japanese, not understand Laos is a country.

I'm not sure... I was giving it some thought and it seems to me to be more the construction of the word itself.

Maltese, Lebanese, Chinese, Japanese, Polish, English, French - AFAICT only used as adjectives.

Canadian, American, Mexican, German, Russian, Nigerian - adjective or noun.

I'm not even trying to touch on appropriateness, just the general rules on how words are used/spelled. Something about 'an' makes it sound natural to use as a noun.

For "English" and "French" we would usually add "-man" or "-woman" ("an Englishman", "a Frenchman"), although people have worried for some decades that the required qualification by sex is too specific.

What was the noun for Japanese?

Japs/Nips, based on Japan/Nippon. These may have always been offensive words, I honestly don't know as it was way before my time, but they both certainly are considered derogatory in the US today.

Which itself is weird, because most other countries we just suffixed - like Englishman, Chinaman(also now considered derogatory, I think), Frenchman, Irishman, etc. But I cannot recall ever hearing 'Japanman' or anything similar.

In any event - I wouldn't take this situation you're in as any slight or bias against any people - it's strictly to do with the English language and ese/ish demonyms.

I thought that these were always considered slang, and that during World War II they became slurs (partly because of their regular use in war propaganda). I don't imagine that there's a time when either term would have been considered a "proper" way to refer to Japanese people, although I do imagine that before World War II they probably wouldn't have been considered insults and might have been considered affectionate.

If my guess about that is right, then you could compare it (pre-WW2 only!) to "Aussie" and "Kiwi" (for Australians and New Zealanders), which nobody would say is "the" name for these groups, but which is also not an insult. Although this is complicated because these are, I think, also autonyms for these fellow English-speakers. Maybe another example is "frogs" for the French, which is mildly disparaging but usually not a horrible insult, at least in contexts that are otherwise respects.

Thank you! There was a very famous Japanese fashion designer named Kenzo Takada. His brand in the 70s was called Jungle Jap. Now the name makes sense!

I wonder if that's intended as a reference to the post-war holdouts

https://en.wikipedia.org/wiki/Japanese_holdout

"Jungle Jap" would be extremely offensive if used by a non-Japanese person to describe a Japanese person today. Although I wasn't born yet, I think that was almost certainly already true in the 1970s.

There are a lot of cases in which people use disparaging group terms and slurs for themselves either as a joke or as a political statement (which is sometimes called "reclaiming" when done consciously and politically). For example, "nerd" is often disparaging but many of my fellow nerds would regularly call each other that in school, and the web comic SMBC routinely refers to its readers as "nerds" (and I don't think the term would be considered disparaging at all when used within the context of a technology-oriented site or forum). I don't think this is a very clever idea for commercial branding, since other people who are aware of the disparaging use might find the brand awkward or uncomfortable!