Thanksgiving, Vow, and Freewill Well-Being Offerings
Paul gives us a genuine bridge: eating a sacrifice meant participation in the altar. That makes Israel's sacred meal highly relevant to Christian table theology without requiring the Bible to say, “Communion = Leviticus 7 fulfilled.”
Where this fits in the story: Explicitly completes the Leviticus 3 shelamim / well-being-offering law.
Where Scripture takes it next: 1 Corinthians 10:16–18 — very strong. Paul explicitly reasons from Israelite sacrificial eating as participation in the altar and places that beside Christian cup/bread participation.