At least through a contemporary lens I didn't get the impression it was political whatsoever. What it did seem to do was fill in the (many) blanks present in the corresponding biblical narratives.
As an aside, I find that PL fills the blanks in the biblical narrative almost too well! There are some aspects of our modern cultural understanding of what angels, demons, and Satan are like that come straight out of PL and have no foundation in the biblical narrative. It leads to a lot of confusion among religious persons because they end up believing in these details that don't come from the avowed authoritative source.
You may have heard a Christian try to claim that Adam ate the fruit after Eve did, with the express purpose of not being separated from her---that he knew she'd be exiled, so he intended to stay with her by being exiled himself. In that way, Adam acquires a sympathetic and heroic tint in his role in the Fall. But this is completely fabricated by Milton! It's straight from PL and nowhere to be found in the biblical narrative.
The poem has a strong republican sentiment (lowercase 'r') throughout. During Cromwell's control, he argued for republicanism; he likely composed much of the early elements of the poem while in hiding after Restoration, fearing very correctly for his life; and he remained a republican for all his life. Milton's characterization of Satan in the poem is incredible because of the way he chooses this unlikely figure to channel so much of his misgivings and criticisms of absolute and monarchical power.
In a modern context, it's fascinating to see how much sympathy Milton can make for Satan (a figure who, in most modern secular contexts, is far more commonly simplistically presented as pure evil incarnate) and how the poem poses evergreen questions about the role and nature of grievance, revolution, vengeance, power, and the masses in governance.
When I read PL at school, Satan came across as a really cool dude who could fly! Admittedly I was (much) younger then.