It definitely is trying to give hints of her being more than mearly "friendly" with him. Poor girl if true, being perpetual third wheel of a world destroying love triangle has to suck.
Sato's mood is similar straightfaced concern towards Aru though. She feels kinda alienated too, like she's proven to not be enough or brave enough to run forward? The convo Sato leaked she's older emphasized that cultural weight too, more older senior sisterly. It's notable she thinks she can persuade the new junior and is a bit awkward with an indestructible brat she can't. (A brat she's had to stalk on hot-mic for years)
Could be more, but I'm wary of reading into it. Though considering style from Nakatani Nio's famous yuri, it'd be darkly funny if Sato is romantically double-doomed.
I can see one potential route. He impregnates her before passing, and then in the final moment she realizes he's still with her via DNA, and the world is saved.