I realize the universal translator is just a hand-wave to avoid the "Aliens Speaking English" trope, but there are at least some basic rules established for it:
When it translates, it will use the closest approximation in the database, it can learn as it hears more of a new language, it's apparently a neural implant (at least with Ferengi), and probably a few more that I'm missing.
Does it keep the original speaker's voice, tone, inflection, and in this case, melody? Does Kira hear Vic singing in perfect Bajoran or is the universal translator belting out Frank Sinatra in Lwaxana's voice? Do the lyrics still make sense with the computer translation?
I very rarely complain about the UT, and I enjoy the Vic Fontaine component, but I just have a hard time combing the two lol.
Sometimes I wish they would have gone with a "standard" language like Space Esperanto that just sounds to the audience like English rather than the UT.
Update: I completely forgot Federation Standard existed, and that's probably the language Vic is using, and Kira is very likely fluent due to her time spent on DS9. It's kind of a retcon since that wasn't mentioned until DIS, but I can live with it.
That could be the case here. Vic may be singing in Federation Standard (aka English) and Kira /Odo have learned it after hanging out with the Federation for the last six to seven years. Considering their backgrounds as people who lived in multi-lingual societies (from the Occupation), it wouldn't be the strangest thing for them to pick up a new language with some off screen effort over the years.
Oh, I don't doubt that many of the characters are polyglots; Kira would definitely be likely to be fluent in multiple languages for all the reasons you said. Perhaps that is the case here specifically, and Vic is singing in Federation Standard.
I also forgot that Federation Standard existed. That's on me ๐คฆโโ๏ธ
No worries. I think you have a valid point and it could also be a weird UT thing going on where Vic's words are translated idiomatically and not literally.