Incidentally, Leia being adopted is public knowledge. Bail and Breha just happened to adopt an infant war orphan just after their heavily pregnant and very close friend Padme died. And said orphan met Palpatine in person multiple times, who would have been able to pick up on her Force sensitivity. At no point did anyone, even Palpatine, ever suspect the Organas were lying because they’re so nice and honest that adopting a war orphan would be extremely in-character and lying about it would be extremely out-of-character.