If she’s on Earth-1 like the Arrow-verse shows other than Supergirl, then why haven’t any of the heroes of Arrow or The Flash or Legends of Tomorrow mentioned any of these characters?
The best move might be to set Batwoman (if the show actually happens) on Earth-38 with Supergirl.
Either way, DC Comics fans can look forward to even more characters traditionally out of Batman stories making their CW debuts.
Kara has already established that Batman exists on Earth-38, so why not Batwoman?