Ezekiel 34 is decisive: YHWH says he himself will search for and shepherd his sheep, while also promising a Davidic shepherd.
Ezekiel 34:11-24; Psalm 23:1 are central backgrounds.
Jesus gathers the divine-shepherd and Davidic-shepherd expectations into his own mission and speaks of the flock as his sheep.
The claim is strong because Jesus fulfills a role Ezekiel explicitly assigns to YHWH himself while also fulfilling messianic expectation.