You pretty much got it spot on, the only thing missing was the extra details that they usually, but not always, had eyes of different colours, and was that they'd always be shipped with the main male character as a way to express the writer's own desires.
Looking back maybe it was a bit problematic too in how it was used by some then, as there was a certain air of 'how dare these girls invade our male fandoms, and they're only doing it cause they want to lock lips with Kirk, Goku, Sasuke, or whoever'. Sure, these fanfics and fanworks were often pretty bad, and it was useful to have a term for them so those not into such things could avoid them, but then plenty of first try fanfics are terrible anyway even with out a Mary Sue to be found. I know mine sure were.
I've certainly seen female creators do loving tributes to the concept as that was often how they got their start, and so want to poke fun at those days when they really didn't know what they were doing, but wanted to do it anyway cause being creative is awesome, so I don't think the term in the original form was entirely a bad thing like it is now where it's just 'I hate this fictional woman'.
I've also seen Casually Comics (great youtuber btw, definitely reccomended) suggest that she thinks that fanfic and related fanworks is in of itself a female dominated part of the phenomenon of fandoms which is why it has sometime been resented by guys in general as an invasion of their space. That I'm less certain on as I've often explored fandoms in that way, and not come across that kind of pushback before, but then again with the way online circles work so many discussions can happen that you'll miss entirely so I'm totally okay taking her word on that in regard to her own experiences of fandom.