So the next question to resolve is: On what evidence do we believe that these verses were interpreted by Second Temple sects etc as having messianic associations and significance?
The Psalms of Solomon, ch. 7 and some DSS scrolls
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How do we determine what a "messianic age" or "messianic person" meant to any group in the Second Temple era? Was there even such a concept as "messianic age" in the Second Temple era? Do we automatically lump every text that speaks of an ideal future as being understood as messianic by groups in the Second Temple era?
I think it meant different things to different groups at various times. The so-called Messianic age (as the advent of an utopic domain for the Jews) also was thought to come without any Messiah.
In Daniel last part, Archangel Michael will bring about resurrections and eternal life. No Messiah here.
I also think there was not much of any Messianic or Apocalyptic expectations when things were going not too bad for the Jews, that is from the building of the second temple, and afterwards under the benevolent and loose rule of the Persians and the Hellenist kings, with the exception of Antiochus IV (whose looting of Jerusalem and ensuing massacres gave us 'Daniel'), up to the Roman arrival in Jerusalem, taking advantage of the late Hasmoneans corruption and in-fighting (that gave us the Psalms of Solomon ch. 7).
At this time, the failure of the Hasmoneans (also with the later Parthian invasion), made some Jews wished for another David, or one of his descendant, from the Davidian dynasty relatively successful in Judah for centuries, to usher better days for the Jews, under rulers of their own.
Then the Herodian kings (non-Jews) came, then the Romans directly. More reasons for wishing an utopic Kingdom under a Davidian king, with God's power to kick out the invaders and keep them outside (as in some verses in the OT). But that does not mean that wishful thinking was general and/or intense among the Jewish population, but only ready to kick in at some appropriate occasion.
Paul had Jesus as from David but that happened in his last epistle (Romans) and I think he reluctantly borrowed that notion from the earliest Jewish Christians (before the divine conception was invented).
Cordially, Bernard