It turns out, however, that for some reason the WP engine itself attempts to be hyper-correct in this case, and enforces an old, Polish standard of having an opening inverted comma/quotation mark at the bottom of the word, and then the closing one at the top of it. Not sure if I can even reproduce it here, anyhow, as it's something that has been largely abandoned in the online era, even in Polish, and most of the websites just use the regular, "two short vertical lines in the top corner of the word" type of an inverted comma, for both opening and closing a quote.
Is there any way I could change this and get a regular quotation marks, without reinstalling WordPress and going for the English version? Just the ones you see on 99% of the websites.
The way it displays right now causes certain issues, e.g. when I want to have a quote in italics, it seems to screw up and puts both the opening and closing quotation marks at the bottom of the word - and that's even though in the WordPress Visual Editor it appears with the more common, online way, i.e. both are on top of the word. I'm trying to enforce the "regular quotation marks", but so far - no luck. It would be so much easier to just input it in a regular way, without having to resort to some trickery for such a minor thing.
Many thanks for the help, really appreciated!