Well, for some of that I imagine it's brand building for Stargirl to be a gateway to buildup stuff like the JSA (like with that Black Adam movie also) but yeah WB can get rather byzantine with their policies on who they let on TV and the movies. I don't watch CW but from what I can tell the most WW stuff they've done is some winks/nods here and there.
I imagine Superman getting a CW show is because Superman as movie franchise seems a less priority for the film division at the moment. Even effected Batman sometimes with the old Bat-Embargo from years back.