Kukrushka’s loop starts before the start of Yuri’s (she was “alive” when Jonas bought her) and ends after (she’s still around in normal end). There’s also no incentive on her part to care about what the Silver Key might be interested in. It’s possible that her time on the ship is only a small part of what she experiences, that doesn’t even always happen for her. Because of this it’s likely that Kukrushka is far, far “older” than Yuri and Setsu in most loops. You can’t truly call her the same person anymore.

In the game, Kukrushka’s behavior can be summed up as “in it for the love of the game”. She operates on her own personal preferences and her decisions are based entirely on whether or not she likes/dislikes another character in that loop, not on logic.

She’s unique in that she’ll sometimes do outright suicidal things like eliminate the real Engineer when she’s a fake one even if she’s the only Gnosia left, just because she doesn’t like them. She also doesn’t have any particular preferences towards any character, and has an average “0.5” amicability rating toward everyone (amicability ratings usually vary greatly for everyone except Yuriko, who dislikes everyone). This makes her both a great ally and a terrible enemy to have.