So from Week 3-4 and the last Issue of Suicide Squad:
The Empress is specifically hunting for Saturn Girl by name. She's been here for YEARS now, having been captured early on and made to serve in a prototype version of the Suicide Squad. After she and the others proved too dangerous, Waller had her buried and locked away in the intervening years.
The Eye runs on the same tech as the Green Lantern Rings, with each freaking out when they encounter each other. Simon Baz nearly destroys the Eye with his ring, so Sarya beats a hasty retreat (presumably the last we'll see of her in this crossover).
She also taunts Superman telling him the future isn't so rosy for him.
Finally the editor's note says the the Empress/Saturn Girl story will play out in .... Supergirl!
https://www.bleedingcool.com/2017/01/11/saturn-girl-new-justice-league-vs-suicide-squad/