Yes, Leslie is wearing the same costume that Ruby Rose's Kate Kane wore during the Arrrowverse show's first season...for now. Leslie promises that her Ryan Wilder, a new character taking up the cape and cowl, is going to "put her own spin" on the Batsuit, which we've yet to see.
As Wilder, Leslie will be stepping into the lead role following Rose's surprise departure from the show after its first season. Kate Kane's disappearance will be written into the story, with Wilder serving as a more "messy" and "untamed" Caped Crusader as she learns the ropes, per DC's first look. Like Kane, she'll be an out and proud lesbian, but she'll also have her own issues, namely being a drug runner who has crossed paths with the GCPD in the past.
In addition to learning how to be a solo hero, Wilder will be thrown into the big leagues, as Batwoman will feature in a two-part crossover with Superman & Lois, which will also introduce her to other characters from the Arrowverse.
The "spin" that Wilder will put on the suit is important, as Leslie and showrunner Caroline Dries revealed during a recent panel at DC Fandome that her official costume would reflect that it's a Black woman underneath the cowl.
Jim Lee may have given us our first look during DC Fandome with an epic poster to commemorate the event.
Like the other Arrowverse shows, Batwoman's new season will premiere on The CW in 2021.