I'm still waiting for that generalization.

THEY ARE NOT ENGLISH WORDS. THEY ARE WORDS UNDERSTOOD AND USED BY ENGLISH SPEAKING PEOPLE.

And I'm asking you what the difference is. What is the metric by which you can determine that one word is an English word, and another word is merely a word understood by English-speaking people?

Since this seems to be yet another non-starter for a productive conversation, here's what you're missing:

A word is an English word when a native speaker of English unconsciously uses that word to another speaker of English with the expectation of being understood.

It doesn't matter what the origin of a word is - it only matters that English speakers use the word with the natural expectation of being understood. So, "Let's go do karaoke" is fine. "Karaoke" is a word of English. "I love eating sushi" is also fine. "Sushi" is a word of English. "Let's hanasu about Lemmy" is not fine. "Hanasu" is not a word of English. This is why "eigo wo hanashiteimasu!" is not English.

(I realize that there is nuance here, for example an anime club using more Japanese words than the general populace. Here we either can say that a word like "bishounen" is a word of English in specific speech communities, or draw a general (but arbitrary) line that a word isn't an English word until X percent of the population uses it fluently. We could also say that "bishounen" hasn't fully become a word of English until that anime fan would use the word to a stranger on the street with the expectation of being understood. Either way, though, it remains the case that English words are defined by usage, not etymology.)

(Note that the same phenomena occur with more "learned" English terms that not everyone knows as well. That is, we see the same behavior between "bishounen" and a lesser-used English word like "adze", just among different speech communities. As such, there's no objectively useful reason to distinguish them, since they show the same pattern of behavior.)

It doesn't matter when the word was borrowed either. Older borrowings and younger borrowings are all adapted to the phonology of English - note that Schadenfreude isn't pronounced in English like it is in German, for example. That's because it has become a word of English, and has changed phonologically in the process to fit the phonological constraints of English.

Further evidence that borrowings become words of their borrowing language is the fact that these words are treated identically to native words by both synchronic and diachronic grammatical processes. For example, sound change is just as regular for borrowed words as it is for native words. Borrowed nouns function in sentences the exact same way as native nouns do. Again, there is no objectively useful reason to distinguish older and younger borrowings, because they behave the same way.

Note, however, that "loanword" is still a useful categorical distinction, since linguistic reconstruction only works on inherited words, and does not work with loanwords or words otherwise created (past the point in history that they entered the linguistic system in question, at least).

But as for a useful categorical distinction between recent loanwords and older loanwords? As long as they're fluently used by native speakers, there really isn't one. (I'll admit that this is a slight oversimplification - we can talk more about this if you're interested.)

HOWEVER, that's not to say that speakers don't have intuitions about borrowed words, because they absolutely do, and that's what I think you're hitting on with your comments here.

"Schadenfreude" and "entrepreneur" feel more like borrowings than "cheese" and "justice" do. This is because the sounds of the word pattern like other words that we "recognize" as being German or French, and the ability to make these identifications are likely also correlated with type/degree of education. The ability to recognize borrowings is also heavily due to spelling conventions, but we have to remember that writing is not language. But that's an essay for another day.

Ultimately, it's important that we realize that the subjective ability to identify a word as a loan does not mean that the word behaves any differently from any other word, and the behavior of language is the only objectively useful means that we have of scientifically describing the structure of language.

Or maybe it's not all that important to realize. But it is the most relevant point in this discussion. Feel free to follow up with any questions you might have.