I’d say the meaning is quite accurate, I usually think of it as “Not really”. Especially and particularly are pretty opposite of the actual meaning so I’d say that’s fine to mark wrong.
Was that what you were asking?
There’s a reason why Jisho translates it as “(not) particularly” . It’s just a difficult word to translate cleanly since negatives don’t work the same in English and Japanese. Some frequency words like めったに have the same issue.
I understand where you’re coming from in terms of how the meaning builds up: strictly speaking, the negative meaning comes from 〜ない. However, since 別に always gets used with a negation, it’s got to the point that you can even say 別に alone in a conversation in order to mean ‘not particularly’. I’m not really sure if we’ve got a word like that in English…
OK, I guess I can’t do it with negation, but I think ‘too’ is a decent example of something similar: it always involves the idea of excess, and often suggests something negative. If you hesitantly look at a present from somebody and say, ‘It’s too…’, that person would expect your next word to be something like ‘expensive’ or ‘flashy’ or ‘sophisticated for me’ or anything else that fits. However, the point is, it’ll be something that creates an overall negative idea, or at least one that involves excess or going, well, ‘too’ far. It’s the same with 別に: because of how it’s used, there are always certain expectations about what’s coming next, even though you are right – it literally means ‘particularly’ or ‘especially’. I’d think of it as ‘(not) particularly’, the ‘not’ being something that will appear later in the sentence.
Yeah kind of piggy backing on others here in my reading experience 別に is almost always used this way (“Not Particularly”). 特別に would be “especially” when I read it because its separate and special from the rest. 別に is like just “this is separate from everything else” and in the case of 別にいいじゃん (which I think is where people get the idea the じゃん is negating things) its a confirming(affirming?) version of じゃない.