Levites get a lot of attention in the first three Parshiyot of Bamidbar.
They are counted in two different ways, given tasks in transporting the Mishkan, purified, and sanctified in replacing the first-born.
Nowadays, they don’t have many duties. One that stands out is the washing of the kohen’s hands in preparation for Birkat Kohanim.
This practice is not mentioned in the Gemara, and Bet Yosef (O.H. 228) brings that the source is from the Zohar. Still, Torah Temima finds a Talmudic source.
תנו רבנן “וילוו עליך וישרתוך” (במדבר יח:ב) בעבודתך הכתוב מדבר… הא כיצד כהנים שומרים מלמעלה ולויים מלמטה (תמיד כו:)
The Levites have their own tasks, such as facilitating song in the Mikdash, but they also assist in Kohanic tasks. Washing is classic service (Kiddushin 22b regarding Avadim) and Birkat Kohanim is tantamount to Avodah לשרתו ולברך בשמו.
Interestingly, the root of this minhag is not arbitrary, but indeed potentially a fulfilment of a Pasuk.