The key is that a Mary Sue is liked by the establishment.

Technically James Bond is a Mary Sue, he's a part of the establishment, extremely competent in almost every aspect, respected by men, and desired by women.

If we take away the trust MI-6 has in him, he would not be a Mary Sue, but the misunderstood outsider who is always right. Dirty Harry perhaps?

The Bond villains are his green aliens.

As for being a writer stand-in, allegedly Bond was a type of wish-fulfillment for Fleming who was not accepted into MI-6.

A Mary Sue is a special type of writer stand in.

It's a character that exists in a world where the establishment fully embraces the alter ego of the writer because they acknowledge the character's competence.