Set in the same universe as Riverdale and The Chilling Adventures of Sabrina.
While Katy Keene and Riverdale are part of the same universe, Katy Keene's time line is set after Riverdale.
As mentioned in the pilot, Josie got introduced to Katy by Veronica Lodge. Josie and Veronica both attended Riverdale High.
During the course of the show, it is exposed that Riverdale's character Veronica is still named Lodge. As the show is set in relative future compared to Riverdale, this strongly suggests that Veronica remained on good terms with her father Hiram Lodge after graduation. At one time during her senior year at Riveridale High, Veronica briefly changed her family name to Luna, in an attempt to break ties with Hiram.
Lucy Hale announced on her Instagram that there will be no second season of the show. (June 2020)