Or HaChaim on Leviticus 9:23/אור החיים על ויקרא ט׳:כ״ג

1 ויצאו ויברכו את העם, They emerged from the Tabernacle and blessed the people. Perhaps they had been commanded to do so by a prophetic vision. It is also possible that the Torah substitutes the word "blessing" here for the word "prayer." The prayer may have been that G'd's Presence should continue to manifest itself in the camp. Even though the people had already been blessed by Aaron, it was good to be blessed by both brothers each of whom represented a different nuance of spirituality, one that is unique to the Levite and the other the spirituality unique to the priesthood. In kabbalistic terms the two brothers Aaron and Moses represented the emanations חסד וגבורה respectively.