Batwoman's teeming writers' room is spectacularly inept at exposition. Or practically anything else; everything in Batwoman -- the plots, the dialogue, the characterizations -- is very comic-booky, in the worst sense of the term.
Unfortunately, a little dramatic coaching might have been helpful as well, because she delivers every line with the same monotonous flatness. Moody is one thing, but numb isn't a particularly engaging vibe.
Batwoman is a solid entrant into the Arrowverse universe and will likely make quick work of finding an audience on the network that has hosted the best live-action DC content for the better part of the 2010s.