Originally Posted by
NeonZ
It has been stated that Barbatos chased Bruce through time though in Metal itself, and that was the Hyper adapter, so I don't think they're different beings now. The idea with Morrison's take was that the Hyper Adapter became a Bat demon/Barbatos due to bonding with Bruce in the future, then falling back into the past, where it then became known as the Barbatos from Dark Knight, Dark City, and I think it still works with the current story.
Barbatos' origin from the newest Metal as the "destroyer" of the Dark Multiverse doesn't really contradict that since his original form there wasn't bat themed either, but just known as "the dragon". So, the only change is that rather than the Hyper Adapter being created by Darkseid (which was never really stated even, it was just the assumption since he pulled it out of nowhere) he just unleashed it on Bruce.