This is the updated Batwoman synopsis via several sources:
In a Gotham suffering in Batman’s absence, Batwoman is a dark DC Comics drama following the journey of Kate Kane as she dons a cape, cowl, and detective’s hat to save her city. But Kate’s personal life proves just as complicated as she grapples with a fractured family, a rookie team, and unattainable love.
Gotham without Batman has been done before. You can see the whole series of “Birds of Prey” to see what that is like. And I actually liked that series. It’s a pity it didn’t go beyond the first season.
I do like the idea for Batwoman and I do hope this becomes a reality.