I'm at work, so can't watch it. But the trailer was posted by the CW, so I guess it makes sense that they'd make it look like it's their show. I'd assume that DCU will make it look more like their show if/when they do any marketing for Stargirl.
I haven't read the books. I did watch the movie but I guess it didn't make much of an impression because nothing on the show seemed very familiar. Except the basic concepts of the alternate earth and the souls in animal form.
I managed to mostly follow the show without book knowledge but it does help when people here in the forum go into more detail about how things are described in the books. Especially as others already mentioned that the town was not abandoned like I thought. And other explanations about how important daemons are which doesn't always come across on the show,