Are the 70 weeks of Daniel and Jeremiah prophecies about the Babylonian exile of the 6th century BC or about the age of the Messiah?

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Jeremiah ostensibly predicted that Israel would be destroyed and be in captivity to Babylon for 70 years:

[Jer 25:11 NLT] 11 This entire land will become a desolate wasteland. Israel and her neighboring lands will serve the king of Babylon for seventy years.

[Jer 29:10 NLT] 10 This is what the LORD says: "You will be in Babylon for seventy years. But then I will come and do for you all the good things I have promised, and I will bring you home again.

The angel Gabriel interprets Daniel’s vision of "seventy weeks" (commonly taken as seventy years) as referring to the captivity followed by the salvation of Israel from Babylon via the Messiah:

[Dan 9:24 KJV] 24 Seventy weeks are determined upon thy people and upon thy holy city, to finish the transgression, and to make an end of sins, and to make reconciliation for iniquity, and to bring in everlasting righteousness, and to seal up the vision and prophecy, and to anoint the most Holy.

In Isaiah’s prophecies it appears that Cyrus is identified as the Messiah who delivers the remnant and builds a new Jerusalem:

[Isa 45:1, 13 KJV] 1 Thus saith the LORD to his anointed, to Cyrus, whose right hand I have holden, to subdue nations before him; and I will loose the loins of kings, to open before him the two leaved gates; and the gates shall not be shut; … 13 I have raised him up in righteousness, and I will direct all his ways: he shall build my city, and he shall let go my captives, not for price nor reward, saith the LORD of hosts.

So did Cyrus fulfill the prediction of the 70 weeks?

Note: What I’m investigating is Paul’s use of the Babylonian captivity and whether he saw the verses he cites as being the original meaning or if he is appealing to the whole of the exile as metaphor/type of the then present "Babylon", Israel.

This paper argues that Paul’s use of Isaiah has its precedent in Jesus citing Isaiah 61:1-2 and Luke 24:25-27, 44-45 and Paul "runs with it", treating Isaiah as a prophecy of his own current day. What I am inclined to proffer is that Isaiah, in its current form, is not about the 6th century BC exile to Babylon and nor is Daniel but rather about the 1st century AD.

But I’m not sure. It seems less contrived to suggest that both Isaiah and Daniel, writing in the context of a Babylonian exile of Israel and the destruction of the city of Jerusalem in his own time. However, there are clues that they were actually predicting Israel’s demise hundreds of years later, in the first century AD.

So which it?:

• the prophets did indeed all speak of the Messiah and the days of the Messiah, or,
• the prophets spoke of their own day and it was "re-heated" by Jesus and Paul to refer to the Messiah and his day and accomplishments

Possibly relevant:

[Act 3:24 KJV] 24 Yea, and all the prophets from Samuel and those that follow after, as many as have spoken, have likewise foretold of these days.