You cannot play Call of Duty: Modern Warfare 2 (2009) map packs on Xbox 360 anymore. The game's multiplayer servers were officially decommissioned, and the DLC is no longer purchasable on the Xbox 360 Marketplace.
Call of Duty: Modern Warfare 2 Campaign Remastered (2020) is a single-player only release on PS4, Xbox One, and PC—it has no multiplayer or maps.
The modern Call of Duty: Modern Warfare II (2022) and Modern Warfare III (2023) are current-gen only (Xbox Series X|S, PS5, PC).