The most accurate “Mary Sue” determinate is whether, at any point in the story, she gives another character a ration of shit. A true Mary Sue is unfailing sweet (boring!) and will endure cruelty yet never retaliate. She gives no one any shit, has little or no agency, and requires rescue. In other words, she doesn’t *do* things. Things *happen to* her. She is passivity personified. The male author-insert counterpart is called a Gary Stu.
Bella Swan is irritable and manipulative. She’s no Mary Sue (but there is a good argument that she’s a McGuffin). Katniss Everdeen doesn’t even come close to qualifying as a Mary Sue.