Even Yisrael by Rav Yisroel Yakov Fisher asks your question as well, and says that the budding staff is to show that shevet Levi is in fact entitles to “more” than the other shevatim, as they get 1/10 (10%) whereas the other shevatim only got 1/12 portion in the land. He goes on to explain why this is, but the budding staff proves that its from Hashem.
Beautiful sefer, and not so hard to understand. Not too long, and not too many things on each parsha. But what he says is often a home run