Generally speaking, modern Mary Sue accusations have sadly become inextricably linked to almost exclusively genders; while some can manage to keep the old meaning, wait long enough and people will start disputing that it should apply to a male character, and start reinforcing its application to a female characters almost exclusively.
I’ve tried in another franchise pointing out how a male character fit the Gary Stu mold more than the female character everyone was gaining up on as a Mary Sue… and it’s clear that part of the reason I got pushback was because even in the old days, “Mary Sue” had a very fluid definition that people can change to suit whatever argument they want.
All the Batcharacters are escapist power fantasies in several ways - but Babs has the temerity to not have a Y-chromosome, so people who want to argue she’s a Mary Sue will immediately choose whatever part of the flexible argument will back them up to do so, while steadfastly ignoring where those same arguments likely apply to their own favorites.
It’s bullshit, but it’s basically what “Mary Sue” means now - a female character scapegoated by a critic with an ulterior motive and a double standard.