Distribution reaches priestly and Levitical households

Kore distributes from the east gate to households, not only to men in courses

Kore son of Imnah the Levite, the porter toward the east, is over the freewill offerings of God, to distribute the oblations of the LORD and the most holy things. Next him are Eden, Miniamin, Jeshua, Shemaiah, Amariah, and Shecaniah, in the cities of the priests, in their set office, to give to their brethren by courses, as well to the great as to the small. Beside their genealogy of males from three years old and upward, even unto every one that entereth into the house of the LORD, goes a daily portion for their service. Priests are listed by the house of their fathers, Levites from twenty years old and upward in their charges, and the genealogy of all their little ones, their wives, their sons, and their daughters, through all the congregation. Also for the sons of Aaron in the fields of the suburbs of their cities, named men give portions to all the males among the priests and to all reckoned by genealogies among the Levites.

Set office means assigned charge, not a modern private office. The lists carry temple-centered administration down to toddlers, wives, and country priests. Genealogical enrollment here is how this house tracked mouths. It does not authorize modern hereditary privilege, gender exclusion, or withholding support from unregistered vulnerable people.

The narrator praises whole-hearted work and then says he prospered

Thus did Hezekiah throughout all Judah, and wrought that which was good and right and truth before the LORD his God. And in every work that he began in the service of the house of God, and in the law, and in the commandments, to seek his God, he did it with all his heart, and prospered.

Chronicles' Hezekiah is a temple reformer whose heart is measured in courses, chambers, and distribution. Kings' Hezekiah is praised for trust, high-place removal, and the bronze serpent; that portrait is not erased by this one. Prosperity here follows this book's account of seeking. It is not a prosperity gospel for later budgets.