What inconsistency? When Railag wants to hurt Biare for killing Shadia, she says that she *is* Shadia – meaning Shadia was entirely her creation.

But was Shadia's biography also created from scratch? A girl comes to Railag and says, "I want to fight you," and when asked, "Who are you?" she replies, "Well, I'm a good assassin." And suddenly, Railag checks her out...
And everyone tells him that there is no Shadia, no one knows her – which immediately seems suspicious. But everything fits together: Shadia existed, her clan was destroyed, and she started taking revenge. Those who die blame Shadia.
Biare, seeing that she can't find a better candidate, decides to use Shadia.
This gives her reputation and allows her to get closer to Railag.

I think that's how it happened.