Signora's hubris was ultimately her undoing, as she lost to the Traveler and was executed by the Raiden Shogun per the rules of the duel. ... With the Raiden Shogun, Signora maintains her professional attitude up until the Shogun prepares to execute Signora for losing her duel against the Traveler.
Why did Signora have to die?
Highly arrogant and sadistic, La Signora is a prideful and narcissistic witch who aims to steal other Gnoses from other gods from The Seven and other nations for unknown purposes. In her defeat by the Traveler, she was executed by Raiden Shogun.
Why was Signora in Inazuma?
Just like in Mondstadt and Liyue, Signora is in Inazuma to claim the Raiden Shogun's gnosis. To do this, she influenced politics in Inazuma to enact the Vision Hunt Decree, destabilizing the islands. With everyone at each others' throats, Inazuma became weak internally, allowing Signora to work behind the scenes.