The term has been watered down so absolutely that I never use it myself... since no one would understand what I meant by it unless I spent extra time explaining it... and at that point I may as well just drop the buzzword and keep the explanation.
I will say that for me it's the "self insert" part that's most important. People forget that the defining trait of the Mary Sue was that she was a way for the writer of the fanfic to lead an idealized fantasy life... and without that very important component you don't have a sue. Rey isn't a mary sue to me, regardless of how some may feel about her talents, because at no point while watching the new trilogy did I look at her, and think "man... JJ Abrams is living vicariously through her."
Likewise, aspirational characters aren't sues to me. Superman isn't a Sue because his status as a paragon who is too good to be real is the point of his existence. He's a symbol of the ultimate good humanity is capable of, and the interesting elements of stories involving him involve him affecting positive change in others. As an aside, that's why grim and gritty, objectivist reframes of Superman fail so bad... well, that and the fact that "objectivist superman" would never be a hero in the first place.
Japanese media has a lot of characters who would be considered Sues by western perspective... pick a light novel, any light novel, basically. I'm not sure if there's cultural context to be had there. I've noticed that, in general -while audiences like to be pandered to all over the world- audiences here in the west like a little bit of subtlety to their pandering... a little bit of plausible deniability so they can try to feel better about their junk food media. Japan largely has no such hangup... their pandering stuff panders completely and shamelessly... for better or for worse.
For western media, the archetype of characters I would be most tempted to label "Sues" is actually a male one. Basically, the one that's made up of characters like Dr. House, Tony Stark, or BBC Sherlock. The self-centered hardass who treats everyone like dirt, but everyone has no choice but to put up with it because, goddamnit! They're the best at what they do, and they know it. That seems to be a bit of a self fantasy brought to life, which fulfills the 'self insert' criteria, and while those three characters do eventually get character development that enables them to ascend from that status to me, there are plenty of less well-written copycats out there.