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This is my first attempt at an answer, so bear with me.
They do seem potentially related. And by that I mean, the earlier betrayal of Judah (by worshipping Ba’al) can be seen as a type of what would end up happening to Jesus. But also, Judas himself can potentially be interpreted as a type for the Jews, as it is Judas (which is the same meaning as Judah, or Yehuwdah) that would betray Jesus. And according to the Gospels, it is the Jews that are described as the ones responsible for Jesus’ death when they called for Him to be crucified.
Hence, Judas AND Judah betrayed Him.
In short, there could be a lot in common between those events.
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No. Despite the names "Judas" and "Judah" being derived from the same Hebrew word "Yehudah", the OT prophecy predicting Judas's betrayal with 30 pieces of silver came from Zech 11:12-13.
Read the NLT translation of Zech 11:12-13:
And I said to them, “If you like, give me my wages, whatever I am worth; but only if you want to.” So they counted out for my wages thirty pieces of silver. And the Lord said to me, “Throw it to the potter” — this magnificent sum at which they valued me! So I took the thirty coins and threw them to the potter in the Temple of the Lord.
But if you read Jer 2:23 in context (Jeremiah 2:1–6:30: Israel’s Covenantal Adultery), it has to do with God speaking through the prophet Jeremiah warning the southern Kingdom of Judah of God's judgment if they persists in idol worship. The fulfillment of this prophecy (i.e. execution of the judgement) already happened in 587 BC (this was when Jerusalem fell to Babylon), about 600 years before Judas's betrayal.
See Overview of Jer 2:1-6:30 below from the ESV Study Bible:
These five related messages were probably delivered during Josiah’s reign (3:6). Jeremiah declares that God’s chosen people commit spiritual adultery by loving idols more than the living God. Thus, they have broken their covenant vows and made themselves ripe for judgment. The prophet asserts that Israel is a faithless spouse (2:1–3:5); Israel can and should repent (3:6–4:4); disaster is coming (4:5–31); there are consequences for Judah’s unwillingness to repent (ch. 5); and God has rejected his people (ch. 6).