Chabad.org — English translation + Rashi
Torah Temimah discusses the order of the two bulls: the word “שני” teaches the relative precedence of blood and limbs of the chatas and olah, establishing the principle that the more sacred item precedes its fellow.
English: Why does the Torah say “a second”? … The blood of the chatas precedes the blood of the olah because it effects atonement; the limbs of the olah precede the emurim of the chatas because they are entirely for the fire. From here: whatever is more sacred than its fellow precedes its fellow.
Gezerah / comparative sanctity — the sequence of the two animals encodes a general rule of priority among sacred acts.
The consecration of the Levites models the broader halakhic principle that greater sanctity takes precedence in order of performance.