There even seemed to be a deliberately Pakula-esque vibe to the music, with certain motifs redolent of the eerie-voice refrains in Klute.
Well it turns out that was even more the case than I thought.
Via Bruce Levenstein, this piece explains how director Sam Esmail deliberately repurposed underscores and motifs from 1970s thrillers (and some later films in a similar vein), despite the enormous cost of doing so.
After learning that, with the later episodes I've spotted a recycled swathe of ruminative, melancholy jazz used in The Conversation (that bit at the end when the Gene Hackman character is thoroughly defeated, hoist by his own surveillance-expert petard etc) and an imposing, stately fanfare (evocative of power and its untouchability) that I'm pretty certain is from All the Presidents's Men or The Parallax View.
But the rest have been more elusive, vaguely redolent of Carpenter or Michael Small but hard to pin to specific.
Ah, stop press - also via Bruce Levenstein - a piece at Indiewire that gives a detailed breakdown of what soundtrack motifs were recycled in Homecoming - turns out I'm right about The Conversation, Klute and All the President's Men. Lots of good-taste choices, including The Andromeda Strain OST by Gil Melle