I don’t think he knows since the king never met her for starters so he can’t have “recognize” her.
I think he simply gave that necklace because it has a strong meaning. They fought for freedom against the king tyranny. The Queen belongs to the royalties that oppressed the people wether she is innocent or not. He is technically using and giving stuff from the old king so I don’t think that makes much differences...
Plus it is not exactly something that personally belonged to the old queen, but rather something belonging to the royalties that was simply past downed to the Queen.
By doing that he is simply indirectly recognizing his brother as such by recognizing his wife as a wife of the Royal familie.
I’m afraid the moment they will discover her identity, shit will spiral down way for a bit
I love your theory, which implies that Cayden is an indifferent king who knows exactly who are his enemies (his father and the old king, I mean). He knows Edna's real identity, but still treats her with good intention (or he simply trusts his brother's hunch?)
Smart characters are always my favourite.

Because he doesn't seem like the type to callously give away jewelry from someone he had a hand in killing. Think he's just trying to get Edna something of her mother's? If that's who the necklace belonged to?