TT points to Menachos / Chullin / Pesachim material on the tenufah of the breast (and later the thigh) (verified via Essential Torah Temimah).
E-Daf examples: Chullin 45a · Pesachim 59b
ידיו תביאינה את אשי ה׳ — כהן מניח ידו תחת יד הבעלים ומניף. החזה — מה שרואה את הקרקע, עד הצואר למעלה ועד הכרס למטה, וחותך שתי צלעות משתי הדפנות. והקטיר הכהן את החלב המזבחה והיה החזה לאהרן ולבניו — אין הכהנים זוכים בחזה אלא לאחר הקטרת האימורים.
“His hands shall bring the fire-offerings of the Lord” — the Kohen places his hand under the owner’s hand and waves. “The breast” — that which “sees the ground”: downward to the neck, upward to the stomach; he cuts two ribs from the two walls. “And the priest shall cause the fat to smoke upon the altar, and the breast shall be for Aaron and his sons” — the Kohanim do not acquire the breast until after the sacrificial fats have been burned.
Custom — procedural detail of tenufah and acquisition sequence.
The breast is waved by owner and Kohen together, defined anatomically, and becomes the property of the Kohanim only after the fats have been burned on the altar.