> 18 million results in Google.
That's not a response. Those results are overwhelmingly not synonymous with the phrase "the poor", which would be clear immediately if you looked at them.
If I search for "the poor people", I get told there are 22M results. The entire first page is taken up by references to a proper noun, The Poor People's Campaign; searching for '"the poor people" -campaign' cuts reported results to 12M, and the new results prominently feature The Poor People's Crusade. This is not a compelling argument that the phrase "the poor people" is permissible in the same contexts that allow "the poor" (which would be necessary if this were a case of ellipsis).
> Another example: "the Chinese people" (we'd just say "the Chinese"), 10M results.
That's a much better example; I'm willing to concede that "the Chinese people" and "the Chinese" mean the same thing and can be used in the same ways. But you haven't made the argument that the equivalence between "the Chinese people" and "the Chinese" transfers over to an equivalence between "the poor people" and "the poor".[1] I claim you cannot do this, because "the poor people" and "the poor" are not equivalent.
Note also that the parallel construction to "the Chinese" is "the Italians", not "the Italian". But we obviously can't claim that "the Italians" is ellipsed from "the Italian people". We also shouldn't claim that "the Chinese" is ellipsed from "the Chinese people".
[1] For one thing, people in "the Chinese people" is not even the same word as people in "the poor people"; "the poor people" uses Merriam-Webster's sense 2 ("plural form of person"), while "the Chinese people" uses sense 5 ("singular noun of which the plural is peoples; a body of persons that are united by a common culture, tradition, or sense of kinship"). https://www.merriam-webster.com/dictionary/people