Is this English translation one of several readings of the French sentence, or is it the only possible interpretation? This particular interpretation seems to suggest that the focus of ne-que is une (tasse), so that it means, roughly, that (1) she made no more than one cup of coffee (and not two or three). Can the French sentence also mean, e.g.; (2) she only made (a cup of) coffee and not (a cup of) tea, etc.; (3) all she did was make a cup of coffee, and she did nothing else; (4) she only made a cup of coffee but didn't drink it; (5) only she and no one else made a cup of coffee; etc. ?
Yes, it's the same problem of interpretation you have in English with placement of the word "only." "Que" or "only" should be placed next to the word to which it refers; e.g, only a cup, only one, only made, only she. It's another of those situations where the context has to tell you what is meant.
"Not but only one" is not a construction I recognise. Is it American? It does not "feel" right, in any case. "But" implies a negative. In the UK we would probably say, "I made but one" (= "I made only one") - but the use of "but one" in this context is obsolescent if not archaic.
Your exact question is in this link, which fully explains the syntax and the 'elegance' as they put it and the comparison with seulement.. https://french.kwiziq.com/revision/grammar/how-to-use-restrictive-ne-que-with-simple-tenses-to-express-only-negative-expressions