Gary stu is a new term for me lol. Didn’t know this version of the whole mary sue trope merited its own term.

But, I’m not actually seeing what you’re asking about. Do you have any female examples?

The closest I’ve seen is someone like Moon Girl or Ironheart in Marvel. But it’s my opinion that the hate they get isn’t because they’re really good at solving problems. They also aren’t really a fulfillment of what you’re describing because they aren’t portrayed as being good at everything. But they’re the closest I can think off offhand.

But I’ll echo other comments. Batman often succeeds by failing first and then figuring out how to counter what caused him to fail. That’s the basic version of modern Batman. Give him prep time, and he’s god tier; surprise him, and you might get away with whatever it is if it’s a one time thing.