Although the Abrams/WarnerMedia deal is definitely going through, it apparently is still being finalized by the attorneys. Ann Sarnoff is officially taking over at WB next week. (Reportedly however she is Abrams' wife's pick, and JJ's wife Katie McGrath also reportedly got Tsujihara canned.)
I actually don't think Cavill is out of the running. They just can't tell Henry anything until Sarnoff is in charge, and the Abrams deal is fully inked. Not saying he has the job. Just that they're still waiting for these changes before they can even broach the subject.
That said, I will hardly be shocked if they opt for anther actor. But there are things in favor of keeping Henry. He's basically popular with the fans as Superman overall, even if many disliked Snyder's approach. He delivers a seriously underrated Clark Kent. He got the Kansas accent down to a tee. It's more grounded versus the Donner/Reeves lovevable dufus mensch (reprised by Brandon Routh in Singer's Superman Returns with disastrous box office results). Cavill's/Snyder's Clark is quite close to what Abrams wanted to do back in 2002.
I think Abrams will do what he wanted to do back then, honestly. It's just that he's fully trusted at this stage to accomplish that in a crowd pleasing way (except for some highly vocal superfans) that critics will applaud. As demonstrated by Star Trek, ST Into Darkness, and The Force Awakens. A lot riding on SW Episode 9--and it's Disney--so it will do mega box office and critics will approve. Probably won't be controversial but rather will restore Luke to what most fans wanted (and Mark Hamill wanted--not that that matters, of course).
The draft of the Flyby script that got leaked I think must have been a version that intentionally set out to shatter many character conventions as a kind of writing exercise, or something. But who knows.