Levi is Leah's third son: "this time my husband will be attached to me, for I have borne him three sons" (Genesis 29:34). The name comes from lavah, to attach, to accompany. Where Reuben and Simeon spoke of seeing and hearing, Levi speaks of the bond.
Jacob blesses him together with Simeon and addresses the same reproach to him: "Simeon and Levi are brothers; their weapons are instruments of violence," and the same sentence: "I will divide them in Jacob and scatter them in Israel" (Genesis 49:5 to 7).
The word of Moses is entirely different: "Your Tummim and Your Urim belong to Your pious one." He praises the one who put the covenant before his own family, "for they kept Your word and guarded Your covenant." Then he gives Levi his mission: "they shall teach Your laws to Jacob and Your Torah to Israel; they shall place incense before You and whole offerings on Your altar" (Deuteronomy 33:8 to 11). The contrast with Jacob's word is striking: the same tribe, the same possible scattering, but now in the service of teaching and worship.
On the breastplate, Levi's stone is the third of the first row, the bareket (Exodus 28:17), which the Targum attributed to Jonathan places under his name. It is often rendered as emerald or carbuncle; the identification remains uncertain. In the desert Levi is not counted with the other tribes (Numbers 1:47 to 49): the Levites encamp around the Tabernacle of the testimony, carry it, set it up and take it down (Numbers 1:50 to 53), and the Tent of Meeting moves "in the midst of the camps" (Numbers 2:17). Ramban links this center to Sefer Yetzirah: "the holy palace set in the middle." Levi therefore has no banner among the four camps.
According to the order of the banners, Levi has no month: the twelve months go to the twelve tribes of the camp, with Ephraim and Manasseh taking Joseph's place (Bnei Yissaschar, Cheshvan 1:2:3). The app, which follows this order, therefore never shows Levi on the main screen. According to the order of birth, the Shem MiShmuel gives Levi the month of Sivan, the month of the giving of the Torah, because of Leah's word: "this time my husband will be attached to me."
Keep this: the tribe that is not counted is the one placed at the center. What was scattering for Jacob becomes, for Moses, the charge of teaching everyone.