This. Everything here needs to be read, and then read again. Especially the stuff I bolded.
Ultimately, this is why comparisons between Snyder's Batman killing, versus Nolan's Batman killing and Burton's Batman killing, are so common and yet so forced. Its not the presence of lethal force, its how the lethal force is contextualized in the story. "What does Batman killing mean?"
In the first Batman movie, its done towards the end of the movie, after a progressively more destructive series of murderous acts by the Joker. Its framed as escalation in the war between the two, with Batman's increasing willingness to kill the Joker and his men paired with the Joker's increasing willingness to kill everyone else. Its set up so that it generally feels appropriate and justifiable, in the context of the movie, particularly since its contrasted to the various earlier scenes- when the stakes were lower, Batman *didn't* kill.
In the Nolan Batman movies, Batman's use of lethal force is often awkward and ambiguous, yes. . . but this is pretty clearly deliberate. The "discussion" of the movies is largely about the ethics of vigilanteism, with Batman's dance upon the razor edge of right and wrong. "What, exactly, counts as killing?" is as important to the movies as "Can you do good in secret?" Also note that, over the course of the movies, Batman's position, and his ability to explain it, changes.
In BvS? As near as I can tell, the only meaning of Batman's lethal force is "violence is cool". I suppose it was *supposed* to be about how Batman has gone off the rails, except that following his Moment of Clarity, he does pretty much the same murderous violence, just with less branding.