> At least through a contemporary lens I didn't get the impression it was political whatsoever.

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.