The monumental task of processing the Passover sacrifices required strict organization and close cooperation among those serving in the Temple. Managing the massive volume of offerings meant that the workload had to be carefully divided to ensure everything was completed properly and on time.
The primary approach among commentators is that the Levites followed a strict order of operations. Their first priority was the general public. They fully prepared the Passover and peace offerings for the rest of the nation according to the laws of the Torah, ensuring that the people would not face any obstacles or commit any errors in their service. Only after the public's needs were completely met did the Levites turn their attention to preparing the sacred meals for themselves and the priests.
The priests were unable to prepare their own food because they were completely consumed by their duties at the altar. Continuously, until the late hours of the night, they were occupied with offering the burnt sacrifices and the choice fats of the animals. Because the priests were tied to the altar without a break, the Levites stepped in to handle the cooking and preparation, ensuring that the busy priests would have food to eat, alongside providing for themselves.
This support system extended beyond the priests. According to [המלבי״ם], the Levites also took on the responsibility of preparing the sacrifices for the Temple singers and gatekeepers. Just like the priests, these groups were strictly bound to their specific posts and were not allowed to leave their duties to prepare their own meals.