Hmm... until they start with the flashbacks I'm gonna assume they're still using Rebirth mixed with elements of the 5G setup in Doomsday Clock Alan's back story, since Batgirls history are still unclear. I'm sure Obsidian and Jade will use their Post Crisis history, so I guess it's a little bit of everything.
About powers and canon, I just remember that while Spectre is considered second only to The Presence, that was when The Hand of Creation was only one and refer to The Presence, but now The Hands are a race of Super-Celestials ranking below The Presence, so The Spectre may be considered in the rank under The Hands instead of under The Presence.
I don't think they ever clear this up in the books, but that's my assumption