The “inner part” means here, not the holy of holies in particular, but the interior generally. The priests alone might enter the temple building. The Levites might penetrate no further than the inner court.
Related Commentaries of 2 Chronicles 29:16
2 Chronicles 29:16
16 And the priests went into the inner part of the house of the LORD, to cleanse it, and brought out all the uncleanness that they found in the temple of the LORD into the court of the house of the LORD. And the Levites took it, to carry it out abroad into the brook Kidron.