Common Mary Sue Traits: Sadie Kane checks most boxes in the "How to make a Sue" Book which is unfortunate considered Riordan had very successfully avoided Sueism in his previous works.
Personality: Highly persuasive, she demanded a rest day all to herself in the middle of preparation for the Apocalypse and everyone agreed, check. Cheerful and "brave" to the point of annoying, check. Rarely get called out, those who called her out was portrayed as wrong anyway, so check. "Just want to be normal",her 2 hot guys become one so they could survive and be with her and she reacted with revulsion; god-like power got treated as annoyance, check . And worst of all, everyone around her can never see her as anything less than perfect: Rude, confrontational and irrationally jealous? Endearing in their eyes. Selfish and at time childish? Wouldn't be Sadie without it.
justified in that the story is told through her narration, so she'd naturally be presenting an unreliable narration - her version of events, if you will.
Power: prodigious magician without training. The first to successfully materialize "Ma'at", the abstract concept other could only hope to understand. Also good with fashion, athletic and life in general.
Appearance: Constant touted as pretty. Get a detail description in her first appearance.
Accessories: her ty'at necklace was one of a kind. And it can glow.
Relationship: her relationship can only be described as Wish Fulfillment taken Up to Eleven: She instantly captured the affection of two prety boys, one of whom is a god who has lived for 5000 thousands years and apparently never knew love until he met her and the other is a guy who has almost given up on life until he met her. And to save her the trouble of choosing, they decided to merge so they can both be with her. Squick be damned.
Story Significance: the chosen one, princess, there'll be no story without her, redeemed Set the god of evil.
One True Threesome: Oddly enough for a kids book. In the end Sadie, Walt, and Anubis come to an arrangement, simplified because the later two now share a body.