If you're finding that you're having difficulty understanding what's going on in this vision of the Beit-Din ha-Ja·dol′ in the heavens on Yom ha-Din, it's a telling indication of just how estranged and alienated you have become from the Original Scriptures in the pretend, self-delusion of idolatrous, Displacement Theology (Hellenism / Christianity). Cf. O·vad·yâh′ 21; Tәhil·im′ 10.16; 22.29 and Dâ·ni·eil′ 7.13-14, 27; 2.44; 7.27.
Several parts of this and the next verse reveal remnants of the underlying Hebrew from which it was translated, and the si·dur′ tradition from which it was taken. It is, therefore, reconstructed back in its original Hebrew from the earliest and most pristine Judaic tradition on the planet today – the Yemenite Jews' tradition.
εγενετο η βασιλεια του κοσμου(egeneto ei basileia tou kosmou; has become the kingdom of the world). However, there is no Hebrew word for "become," ruling out the concept of "become a kingdom of the world." A priori, simply being in Greek demonstrates that it is a Hellenist paraphrasing of המלכות של העולם הבא (ha-Ma·lәkh·ut′ shël ha-o·lâm ha-bâ; the Kingdom of the world to come). Further, confusion among Greek-speaking Hellenist (=idolatrous) Roman gentile Christians concerning the various translation traditions (of the underlying Hebrew) that were floating around among Christians even centuries later is evidenced by the variant readings of the earliest extant mss. Εγενετο η βασιλεια (egeneto ei basileia; kingdom is become) is preferred according to א, P-47 and most early mss., rather than the later εγενοντο αι βασιλειαι (egenonto ai basileiai; kingdoms are become), as found in Textus Receptus of 1624 C.E. based on ms. 1 (12th century).
The concept of העולם הבא described as the מלכות of י--ה and His משיח was so obviously the underlying Hebrew that it jumps out from the Greek paraphrasing to the reader who is familiar with both.
The subsequent phrase is even more conspicuously taken from the Hebrew si·dur′ : י--ה ימלוך לעלם ועד
This phrase is found in the si·dur′ in the Yom Tәru·âh′ Mu·sâph′ Âl·ei′ nu prayer: